Sample Problem: Solving Algebraic Equations

Example:

• a + 1 = 3
• a = 3 - 1
• If you transpose a certain value to the other side of the equation, it "becomes the opposite of the original," so plus becomes minus, minus becomes plus, multiply becomes divide and vice versa.
• a = 2
• 2 + 1 = 3
• 3 = 3
• a = 2

Sample Problems:

• Solve for a:
• 5 + a = 7
• a - 13 = 4
• 3a  = 9
• a/2 = 10
• Solve for b:
•  9 + b = 15
• b - 2 = 1
• 2b = 2
• b/3 = 4
• Solve for c:
• 6 + c = 13
• c - 3 = 2
• 2c = 20
• 6/c = 3
• Solve for x: 
• 2 + x = 24
• x - 3 = 20
• 8x = 16
• x/7 = 5
• Solve for y:
• 8 + y = 28
• y - 4 = 12
• 3y = 15
• y/8 = 2

Sample Problem: Substituting Variables

Example Problem:

• What is the value of a + 1 if:
• a = 1
• a = 2
• a = 3
• a = 4
• a = 5

Answer to Example Problem:

• a + 1 =
• 2
• 3
• 4
• 5
• 6

Sample Problems:

• What is j + 7 if...
• j = 5
• j = 9
• j = 6
• What is u + 5 if...
• u = 4
• u = 2
• u = 8
• What is d + 9 if...
• d = 5
• d = 2
• d = 11
• What is b + 6 if...
• b = 1
• b = 4
• b = 3
• What is x + 8 if...
• x = 1
• x = 2
• x = 3

Sample Problems: Variables

Here are some sample problems regarding the previous discussed topic: Variables.
Try to answer the following orally and as fast as you can. Ready... get set... go!

• Try to identify the variable(s) in the following expressions:
• a) 7j + 8
• b) 5x - 2
• c) 9a + 3b
• If x represents the number of meters Nick sprinted for gym class, make an expression for:
• a) The distance Nick sprinted, doubled.
• b) Half of the distance Nick sprinted.
• c) The distance Nick sprinted, plus an additional 10 meters.
• If y represents the number of hours Jane spent sleeping, make an expression for:
• a) 5 hours more than the number of hours Jane slept
• b) Twice the time Jane spent sleeping
• c) Twice Jane's time sleeping, plus 5 more hours
• If z represents the number of gun shots James fired, make an expression for:
• a) The number of shots James would have made if she fired 8 more shots.
• b) The number of shots James would have made if she only fired half of the total shots she did.
• c) The number of shots James would have made if she fired 3 less shots.
• If x represents the amount of money (in PHP) Julia spent at the bookstore, make an expression for:
• a) The amount of money she would have spent if she bought one more book worth 280 pesos.
• b) The amount of money she would have spent if she didn't buy the book worth 150 pesos.
• c) The amount of money she would have spent if she had spent twice as much, and bought an additional book on sale for 75 pesos.

Done with the excercise? Still remember your answers? Wanna know how many you got correct? Wanna check if you even managed to get all the questions right?

Read ahead to see the answers!

Variables

Variables are symbols that represent a number in algebraic equations, problems, etc. Usually, they are letters but sometimes they could also be letters of the Greek alphabet, or if you'd like, they can be drawings, if you're really that creative! As I've said, a variable can represent any number, so...


Example:

• In the algebraic expression 5 + a , a is a variable and represents any number.
• In the algebraic equation 7 (a) = 28 , a is a variable that, based on the equation, represents the number 4.
• To check if this is correct, we replace the a with 4, thus making the equation 7 · 4 = 28

Usually, we use variables for when we are talking about unknown quantities.

Example:

• I know that John is 5 years older than his sister Jane. However, I do not know how old Jane is. So, if I were told to write John's age based solely on what I know, I would have to write it as 5 + x , with x being Jane's age, which is the unknown quantity keeping me from finding out how old John is.
• If a friend tells me my book weighs 3 times more than hers, but I do not know how heavy her book actually is, then I guess I'd have to write it down as:
• x representing her book's weight
• 3x for my book's weight, which is three times heavier than hers.
• If Sam grows 5 cm more, he will finally be as tall as Pam who is 160 cm tall. This statement says that Sam's current height plus 5 cm is equal to 160 cm . Thus, we shall write
• x + 5 = 160 which represents Sam's current height
• and, upon solving the problem, we come to find out that x = 155
• Therefore, we now know that Sam is 155 cm tall.

Note:

• Remember that algebraic expressions and equations can contain more than one variable.
• Example:
• 2 × (a · b)
• This algebraic expression contains two variables: a and b

LAMEFHM Year-End Special: We're Continuing Our Review Program! :)

First of all, hi. As you all know, the LAMEFHM Team is dedicated to making linear algebra easy. But truth is, we'd also like to help out our dear readers--yes, that's you!--understand math itself, not only linear algebra. Plus, we gotta face the facts here: if you don't really understand the few basics of math, then buddy, you'll definitely have a hard time with linear algebra and, most probably, a lot more of the other more complicated and complex maths you'll encounter beyond your elementary and high school years.


As our year-end special, we've decided to continue our review program! The review program I'm talking about is the one I've mentioned on the first post of this blog, wherein we intend to publish posts here concerning few of the basic math concepts.


So, you folks better be ready for a lot of posts comin' up all about math! :) Hope you guys enjoy.


BELATED MERRY CHRISTMAS, by the way, TO EVERYONE!


And


HAPPY NEW YEAR!


Though kind of late...

We wish you a Merry Christmas;
We wish you a Merry Christmas;
We wish you a Merry Christmas and a Happy New Year.
Good tidings we bring to you and your kin;
Good tidings for Christmas and a Happy New Year.
♥

QOTW from Richard van der Merwe

Quote of the Week

or rather.. "Joke of the Week" :))

Hello guys! Ktine here once again! :P We'll post a tutorial video soon, since Pam is now in the process of editing it. Plus, we have a surprise for you readers.. You have to study for it though. Wait for future announcements!

PAM: The Sum & Product Of The Roots Of A Quadratic Equation

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ஜ۩۞۩ஜ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
Yowee. ^^

As you guys have noticed, I rarely—scratch that, I meant barely—post tutorial videos here in lameFHM. Why? Well, it’s not because I’m too lazy & it takes so much time & effort to create a single video. Not because it’s exams week/ UPCAT (or any college entrance exam, for that matter) week/ school-activities-galore week. And, certainly not because I want to spare the diminutive dignity I have left.

It’s actually because I’ve been waiting for Karlea Khristine Julia Marquee any one of my group mates to be a guest star in my next tutorial vid. At this point, I've realized that that is highly impossible and quite unattainable because, apparently, the reason why they gave me this portion of the website is to save their own reputations for the sake of their grandchildren and sacrifice mine instead. Just kidding. I'm forever grateful for being a part of this website. Love & thank you guys! :)

Anyways, enjoy watching this old video entitled Abobo & The Big Bad Bitch. I made this, along with my group mates including Khristine, way back in 2^nd year for a math subject project as well. :)

Kudos (Oh wait, I don’t have that any more, do I?)!

Love,

Pam ♥

P.S. Have you guys noticed our new layout? I totally Pamela-fied it. ^^

Abobo & The Big Bad Bitch

Part 1: http://www.youtube.com/watch?v=xMyUpYrKyDQ

Part 2: http://www.youtube.com/watch?v=uytdFLXj-Vc
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Quote of the Week

To most outsiders, modern mathematics is unknown territory. Its borders are protected by dense thickets of technical terms; its landscapes are a mass of indecipherable equations and incomprehensible concepts. Few realize that the world of modern mathematics is rich with vivid images and provocative ideas. ~Ivars Peterson

Ktine here once again. I'm sure you're missing
Derpina, am I right? DO NOT FRET MY DEAR MINIONS. I'll upload a comic strip soon.(oh and Pam keeps on insisting that we act as guests in her next video. (I honestly think that we're not needed to make another tutorial video though. Pam's greatness in mathematics is enough)

EXAMs WEEK! *Dun dun duuuuuun*

Hello, ea again. In behalf of our team, we are deeply sorry for making you guys miss us (awwww) It's exams week here!!!! Hahaha. Hopefully, we've been a big help for all your mathematical needs!


We will resume updating on Monday!





Goodluck to us! :)

A surprise awaits those who have been supporting our blog :)

Hello! Karlea here :)

The LAMEFHM team has a surprise for our committed viewers and subcribers.

Drum roll pleaaaaaaase.

*Danandandandandandandnanandan*

*insert drum solo here*

In  just a few more hours...

(guess what?)

"There's gonna be a zombie apocalypse!!!" ..I wish! >:D Try again ^_^

"Unicorns finally came into existence?"  ..Sorry for crushing your hopes and dreams but, Nooooo :P

Tired of guessing? 

To thank all our readers, the LAMEFHM team came up with a brand new section for the blog.

It's still a surprise though! :D

Hold on to your mouses and be ready to be emotionally and mentally awed by the surprise.

To make it more interesting, I suggest you guys study up for it!

I'll say Goodbye for now!

Stay tuned for the big surprise! :D

Again, Karlea here. Signing out :)

*insert smoke effects*

Teehee XD

Quote of the Week

Hey guys! Ktine here(once again). We are so sorry for not updating lately... School work and entrance exams have been keeping us busy. T^T Our friend Pam,(if you remember the pretty white girl who looked funny in the math tutorial she posted here) was supposed to post a new tutorial, but I have no idea if she'll post. You don't need to fret though, since I'll continue pestering her until she posts it. >:)


I hope this quote'll inspire you guys out there, like me(who is "mathematically challenged")

"There are two ways to do great mathematics. The first is to be smarter than everybody else. The second way is to be stupider than everybody else -- but persistent." -- Raoul Bott

Karlea's Korner

Hello! Karlea here. (if you dare mispronounce my name, I will.... hug you until you can't breathe and you will therefore suffocate within my arms and.. teehee. NVM) You guys can call me Ea (eh-yah).
.
.
.
.
.
...prepare yourselves for utter RANDOMNESS!! haha.
Subscribe everyday to our blog for exciting posts about Linear Algebra and everything and anything there is to find.. for I will blur out your stress from numbers and variables by shooting them with rainbow, butterflies and pure RANDOMNESSS!!!! 
*insert rain of confetti and gunshots here* 


For now, I will leave you guys with a short story of what the everyday lives of your beloved LAMEFHM staff goes like.

1

2

3

*click*

"FAILURE"
*the LAMEFHM people are all frustrated about a test or something*


Karlea: My lungs are failing..
Marquee: ....?
Karlea: My kidney's failing..
Ktine: Whaaat?!
Karlea: MY WHOLE LIFE'S A FAILURE!
Marquee: (LOL-ing)
Ktine: (LOL-ing, too)
Karlea: I'M A FAILURE! :(( *BOOKHOO*
(Everyone laughs)
----------------------------------------------------


Wooops, that's all for now. If you didn't laugh, well.. BLAAAAAAAM! Hahaha.
I'll get you guys the next time. Until then :p
Once again, Karlea/Ea here, signing off.
*wave* 
TEEHEE OuO

Quote of the Week

Hi! Ktine here. We are so sorry for not updating LAMEFHM that much this week. School has been very mean to us.

The Equation of earnings

Engineers and scientists will never make as much money as business executives. Now a rigorous mathematical proof has been developed that explains why this is true:

Postulate 1: Knowledge is Power.

Postulate 2: Time is Money.

As every engineer knows,

Work = Power * Time

Since Knowledge = Power, and Time = Money, we have:

Work = Knowledge * Money

Solving for Money, we get:

Money = Work / Knowledge

Thus, as Knowledge decreases, Money increases, regardless of how much Work is done.

Conclusion: The Less you Know, the More you Make.

Note: It has been speculated that the reason why Bill Gates dropped out of Harvard’s math program was because he stumbled upon this proof as an undergraduate, and dedicated the rest of his career to the pursuit of ignorance.

PAM: Linear Equations with n Variables

Linear Equations With n Variables

An Introduction On Matrices

Hey guys. Since we are talking about Linear Algebra here, let's go with what we call a "matrix".

First of all, what is this Matrix?

 Secondly, NO.

It is not the movie with Keanu Reeves. I'm not going to give you a dictionary definition of matrix, but I'll instead give you a picture.

Tadah. That's a matrix. Looks pretty simple, right? There's a general formula for the matrix, but then you'd just scratch your head and go "WHAT?!", so I'm just gonna give you the intro.

A matrix, like any other thing in the world, has parts. There're the

• ROWS
• COLUMNS
• MAIN DIAGONAL
• ELEMENTS OF A MATRIX
• UPPER TRIANGULAR OF A MATRIX
• LOWER TRIANGULAR OF A MATRIX

These parts are pretty easy to define. Elements are just the numbers/things inside the matrix. If you cut a matrix in half, the elements run over is the main diagonal. Then, like a sandwich, there's the upper part and lower part cut off. Those are the upper and lower triangular of a matrix. Nothing much, really.

Now, why would we need to learn these matrices, anyway? We've already got this:

And that's just one of the formulas to remember. It's pretty simple really, with the matrix, you can:

• Solve as many linear equations as you want!
• Find the correct quadratic equation for those pesky graphs!
• Balance a chemistry equation with an actual formula!
• Always know where you are, thanks to your GPS (global positioning system)!
• Watch all those 3D movies, thanks to the matrix!

So you see, the matrix has many, many uses in everyday life. Well, now that you've gotten oriented to the matrix, let me teach you how to name a matrix.

It's pretty simple really, the number of rows X number of columns. For example:

This matrix's name is 4X6. There are four rows and six columns. See? It isn't that hard.

However, the next step to learning the matrix is quite tricky. Do we use operations on matrices as a whole?

The answer is YES. We do.

However, that topic will be tackled on another day. For now, just enjoy transposing from Keanu Reeves to looking at bunch of rows and columns on a board.

Thanks for reading! I hope you learned a whole lot from this segment!

Derpina's adventures w/ Linear Algebra 1

Quote of the Week

An engineer, a physicist, and a mathematician are shown a pasture with a herd of sheep, and told to put them inside the smallest possible amount of fence. The engineer is first. He herds the sheep into a circle and then puts the fence around them, declaring "a circle will use the least fence for a given area, so this is the best solution." The physicist is next. She creates a circular fence of infinite radius around the sheep, and then draws the fence tight around the herd, declaring, "This will give the smallest circular fence around the herd." The mathematician is last. After giving the problem a little thought, he puts a small fence around himself and then declares,"I define myself to be on the outside."

Simple Simplification

Simple Simplification is just Simply Simplifying.

Students are often told to "simplify their answers" or to provide their answers in their "simplest form" ... What does this mean, exactly? With Algebra, that usually means you have to combine like terms. Like terms are terms with the same variables and possibly exponents, but sometimes with different coefficients. Since they're like that, we can mix 'em together.

Example:

• 7x and 5x are like terms, which means we can combine them to form 12x. Don't worry, this won't change the its value. Here, let me show you:
• 7x + 5x = 12x
• Let x = 9
• 7(9) + 5(9) = 12(9)
• 63 + 45 = 108
• 108 = 108
• But, if in case it were 7x and 5x², we can't combine them because their variables are not like terms, because their variables aren't the same (since x ≠ x²). Get the idea? Let's have more examples.
• 7x² + 5x + 9y² + 6y = 428
• Can you combine any terms in this equation? No. There are no like terms in that equation.
• 7x² + 5x + 9x² + 6x = 428
• Can you combine terms? Yes. We can simplify this equation to come up with: 16x² + 11x = 428
• 7x + 5xy + 9y = 6
• Are there any terms we can combine here to simplify the equation? No. We can't combine 7x with 5xy even though they both have x because 7x doesn't have y and we can't combine 9y with 5xy even though they both have y because 9y doesn't have x.

Try to simplify the following:

• 3x + 4x
• 2y + 3y
• 4a + 5a
• b + 5b
• 4xy + 7x² + 8y² + 2xy + 5x - 6y - 9y

Answers:

• 7x
• 5y
• 9a
• 6b
• 7x² + 5x + 6xy + 8y² - 3y

Note: When faced with more difficult problems, please refer to two of our previous posts regarding Properties of Equality and Properties of Operations & Identities. Who knows, they might help you in ways you never expected. :)

About our Next 'Magical' QOTW

Snapshot taken from Marquee's comment at Simple Words to Magical Algebra.

There you have it, folks! One of our blog contributors had already put up an early "Easter Egg" for y'all about out next Quote of the Week (QOTW)! Isn't this exciting? So, be sure to tune in to LAMEFHM and keep yourself updated every Wednesday for more of our awesome Algebra quotes! And, feel free to just keep those comments comin'. We're more than happy to hear from our readers!

Simple Words to Magical Algebra

In case most of you are wondering what to do when your Algebra teacher gives you a quiz and decides to dictate the questions in sentences... well, don't fret, LAMEFHM is here to help! With this post, we'll show you how to turn simple words to algebraic expressions and/or equations and solve problems!

Don't worry, your teacher is not crazy by dictating stuff instead of writing the number problems on the board during your quiz on Algebra. That's normal. And there's a way to solve it! Mathematical word problems are most commonly solved by translating them into expressions and equations or, as I like to call them, "algebraic sentences."

Here's an example for you:

• Your teacher says... "I bought a coffee maker for $50 after they deducted $20 from its original price because it was on sale and had a discount. How much was the original price of the coffee maker I bought?" (Credits to TutoringMaths for the cool image and to Basic-Mathematics for their awesome word problems!)

To solve this, you have to write it as an algebraic sentence (meaning write it as an expression or equation). To do that, you have to:

1. Distinguish the quantity missing or unknown. Know what you're trying to find. (This is usually what your teacher asks you to find.)
2. Get variables to represent the quantity you're looking for. (Usually, the most common variables used are a, b, c, x, y, and z.)
3. Find out what kind of operations you have to use in solving the given problem.

Following the steps mentioned lets you know that:

1. The original price of the coffee maker my teacher bought is unknown. I must try to find out how much that coffee maker originally cost!
2. I'll get the letter x (since the letter x is so cool) and use it as the variable to my equation (you'll be using an equation instead of an expression with this problem... I'll explain why later) and name the unknown quantity x, making x = original coffee maker price.
3. I'll be using subtraction with this problem ... and let me show you why subtraction is the operation I'll be using... later.

Ready to know the answer? Let's solve!

• x = original price
• x - 20 = 50
• We subtracted 20 from x since x is our original price, and the teacher said he bought his coffee maker with a $20-discount for $50. Subtract $20 from the original price and we get the amount the teacher paid for his coffee maker which was $50.
• x = 50 + 20
• Since $50 is the price of the coffee maker once the $20-discount has already been deducted from its original price, we therefore transpose 20 (since we only need x to be the only one remaining on one particular side of the equation in order to come up with its value) to the other side of the equation (and since we transposed it to the other side, its sign changes, hence the plus sign instead of the minus) and add 20 to 50 to come up with the original price of the product before the $20-discount has already been deducted.
• x = 70
• Here we now have the answer, which is $70 as the coffee maker's original price before its $20-discount has already been deducted.

We here at LAMEFHM hope our posts help--especially this one, since this one was originally created to help--you... so, if you've got questions or more ideas/suggestions/opinions/comments/messages regarding how you think we can be more helpful to you and your mathematical needs... just leave a comment and we'll answer as soon as we possibly can! Thanks! :)

Properties of Operations and Identities

• Commutative Property of Addition
• a + b = b + a
• Example:
• a + b = b + a
• a = 7
• b = 5
• (7) + (5) = (5) + (7)
• 12 = 12
• Commutative Property of Multiplication
• ab = ba
• Example:
• ab = ba
• a = 9
• b = 6
• 9 · 6 = 6 · 9
• 54 = 54
• Associative Property of Addition
• (a + b) + c = a + (b + c)
• Example:
• (a + b) + c = a + (b + c)
• a = 4
• b = 1
• c = 2
• (4 + 1) + 2 = 4 + (1 + 2)
• (5) + 2 = 4 + (3)
• 7 = 7
• Associative Property of Multiplication
• (ab)c = a(bc)
• Example:
• a = 9
• b = 8
• c = 5
• (9 · 8) · 5 = 9 · (8 · 5)
• (72) · 5 = 9 · (40)
• 360 = 360
• Distributive Property of Multiplication Over Addition
• a (b + c) = ab + ac
• Example:
• a (b + c) = ab + ac
• a = 12
• b = 7
• c = 5
• 12 · (7 + 5) = (12 · 7) + (12 · 5)
• 12 · (12) = (84) · (60)
• 144 = 144
• Additive Identity Property
• a + 0 = 0 + a = a
• Example:
• a + 0 = 0 + a = a
• a = 5
• (5) + 0 = 0 + (5) = 5
• 5 = 5 = 5
• Multiplicative Identity Property
• 1(a) = a(1) = a
• Example:
• 1(a) = a(1) = a
• a = 3
• 1(3) = 3(1) = 3
• 3 = 3 = 3
• Quotient Property
• a (1/b) = a/b
• Example:
• a (1/b) = a/b
• a = 1
• b = 2
• 1 (1/2) = 1/2
• ½ = ½
• Multiplicative Inverse Property
• a (1/a) = 1
• Example:
• a (1/a) = 1
• a = 3
• 3 (1/3) = 1
• 1 = 1
• Multiplication Property of Zero
• 0(a) = a(0) = 0
• Example:
• 0(a) = a(0) = 0
• a = 1
• 0(1) = 1(0) = 0
• 0 = 0 = 0

Properties of Equality

• Addition Property of Equality
• If a = b and c = d, then a + c = b + d
• If the value of a is equal to b, and c is similar to the value of d, then adding a and c is equal to the sum of b and d.
• Example:
• a = 1 and b = 1 therefore we can say that a = b ;  c = 2 and d = 2 so we can say that c = d
• a + c = b + d
• 1 + 2 = 1 + 2
• 3 = 3

• Subtraction Property of Equality
• If a = b and c = d, then a - c = d - b
• It's just like how the Addition Property of Equality works except, only this time with this property, you're going to subtract instead of add.
• Example:
• a = 1 and b = 1, a = b ;  c = 2 and d = 2, c = d
• a - c = b - d
• 1 - 2 = 1 - 2
• -1 = -1

• Multiplication Property of Equality
• If a = b and c = d, then ac = bd
• Example:
• a = 1 and b = 1, a = b ;  c = 2 and d = 2, c = d
• ac = bd
• 1 · 2 = 1 · 2
• 2 = 2
• Division Property of Equality
• If a = b and c = d, then a/c = b/d and a/b = c/d
• This property is kinda the same with the other properties previously mentioned since it says that if the value of a is equal to b, and c is similar to the value of d, then a divided by c is equal to b over d. The extra thing that this property has is the a/b = c/d equation. What does that part say? Well, since a = b and c = d, a/b would be equal to 1, and so would c/d. Therefore, since both are equal to 1, a/b = c/d.
• Example:
• a = 1 and b = 1, a = b ;  c = 2 and d = 2, c = d
• a/c = b/d
• ½
   = ½
• 0.5 = 0.5
• a/b = c/d
• 1/1 = 2/2
• 1 = 2
• Reflexive Property of Equality
• This property states that a = a
• Well, this property speaks for itself. If it's a, then it's a. It's kinda like how you are you. a = a. 1 = 1.
• Example:
• a = a
• 1 = 1
• Symmetric Property of Equality
• If a = b, then b = a
• Since a is similar to b, then b is also similar to a.
• Example:
• a = 1 and b = 1
• a = b and b = a
• Transitive Property of Equality
• If a = b and b = c, then a = c
• Example:
• a = 1 and b = 1, a = b ;  c = 1, b = c
• a = 1
• b = 1
• c = 1
• a = b
• a = c
• Substitution Property
• If a = b, neither can be substituted for the other to find the value of the other.
• This one's kinda tricky to explain with just words, so look at this example to understand the property more.
• Example:
• x = y + 5
• If: y = 7
• x = (7) + 5
• x = 12
• Zero Product Property
• If ab = 0, then either a = 0, b = 0 or both a and b = 0
• This property says that if you multiply two variables together and their product is zero, then that means that either one of those variables are equal to zero (since they yielded a product of zero), or both of their values are zero.
• Example:
• ab = 0
• If: a = 9
• b = 0
• If: b = 6
• a = 0

Algebra: T&D

Important T&D (Terms and Definitions) for Algebra:

• Algebraic Equation - an equation that can contain one, two or even more variables.
• Equation - has two expressions that are equal to each other.
• Algebraic Expression - an expression that, like the algebraic equation, can contain one, two or more variables.
• Expression - a phrase representing a number.
• Variable - a symbol (usually a letter) that is used to represent the (missing) value or number.
• Coefficient - the number that is multiplied by the variable.
• Example: In the term 5x, the variable x has a coefficient of 5.
• Constant - a term with no variables
• Like Terms - terms with the same variables and possibly exponents, but sometimes with different coefficients.
• Null Set or Empty Set  - denoted by the symbol Ø, it is a set that has no members, hence its name.
• Replacement Set - set with values from which to find a solution.
• Simplified Form - the result of the expression once all like terms in the expression had already been combined and is still equal to the original expression.
• Reciprocal - the reciprocal of a number n is one over that number or 1/n, and once a number is multiplied by its reciprocal, the resulting product should be equal to 1.
• Solution - any value for the variable that makes the equation true.
• Solution Set - a set that contains the variables that will make the stated equation true.

Quote of the Week

Hello! Welcome to the site (as previously said by Julia).

Here, Linear Algebra becomes normal English instead of mathematical Jargon. That's all I have to say I guess.

Quotes are posted every Wednesday. :)

Back to Basics

Salutations!

So, as you can see, our website is still quite new and since this is just our first post, we thought we'd give crash-course recaps to some of the maths topics you've all probably already encountered (and so have we) before getting into your Linear Algebra classes.

Why did we decide to do so? To make sure that you're already familiarized and/or your mind is refreshed with information regarding most of what we'll talk about here. And, since we're still just beginning our Linear Algebra lessons as well, we still need a lil' bit more time to understand, know the explanations, type, explain and educate, and publish posts all about Linear Algebra!

So, while everything else is still going on, enjoy and have fun with our pre-Linear-Algebra posts, topics, lessons and recaps! :)

Love, The Linear Algebra Made Easy For Hard Math (LAMEFHM) Team!

Credits to Google Images!