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### Course: Precalculus>Unit 7

Lesson 1: Introduction to matrices

# Intro to matrices

Take the red pill and enter the Matrix! Created by Sal Khan.

## Want to join the conversation?

• Can a matrix have an expression or an equation? What about variables and complex numbers, can it have those too?
• Basically, a matrix is just a type of table. You can put in the cells whatever you like, but to preserve all the functionality of a matrix, it should be possible to multiply and add up each cell with any other.
For example, it would make little sense to multiply "y=x+1" with "j=3r".
• Is there a difference between the Scalar "1" and the Matrix [ 1 ] ?
• Yes it is like difference between the 1 apple and 1 basket with 1 apple :)

you have still the 1 apple, but you look at it as 2 different things. On left side, the "Scalar '1'" and on the right side you have 1 basket containing 1 apple: "Matrix [1]"
• Is it okay to have decimal numbers in matrices because every video you have has shown whole numbers inside of the matrices
• The examples use integers (whole numbers) because the math is less complicated so it makes it easier to explain without getting lost in more difficult calculations.
Yes, you can have decimals or fractions in a matrix. When you find the inverse of a matrix, you almost always have fractions (or decimals) in the resulting matrix.
• Hopefully this is the right place to ask this question. What are the elements of a matrix and how is it found?
• the elements of a matix are the numbers in the matrix. How are they found? - well, they just ARE. - you could create a matrix yourself...and that it how itd be "found"
• Didn't Sal spell the word " columns" wrong at ?
• Nikki,
Yes, at he misspelled "columns" carelessly omitting the "n". Sal makes mistakes just like you or I do. None of us are perfect, even Sal. But at Khan Academy, we can keep trying to get closer to perfect. My careless math mistakes dropped substantially when I was forced to get 10 questions in a row correct to be proficient in a skill at Khan Academy.
• What is an "array"?
• An array is just a simple picture with rows and columns to represent a value of something.
• In a Matrix can there be varibles like x so 4 0
x 7 or not ?
• Yes, and in some fields of mathematics, they are used often. Linear equations can be expressed as matrices:
4x + 2y = 3
2x -- y = 4
would be the matrix equation
| 4 2 | * | x | = | 3 |
| 2 -1 | | y | | 4 |

(I hope the formatting turns out on this. I'm a novice to commenting and am not sure how to display a matrix in-thread. If not, it's a 2x2 of 4, 2, 2, -1 times a 2x1 of x, y set equal to a 2x2 of 3, 4.)
• can you use pie or 3.14 in the matrix
• Luis,
You can use pi (π) in a matrix. In the first matrix in this video, Sal used π as the value in the second row, first column.
You can also use decimals such as 3.14.

3.14 is only an approximate value of π so if you used 3.14 when π was the exact value, you would be using a approximate value and not the exact value.

I hope that helps.