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Algebra

Notation of matrices- Home
- Linear Algebra
- Linear Equations with Matrices

Still Confused?

Try reviewing these fundamentals first

Algebra

Notation of matricesStill Confused?

Try reviewing these fundamentals first

Algebra

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Get Started Now- Intro Lesson3:21
- Lesson: 1a2:37
- Lesson: 1b1:26
- Lesson: 1c8:33
- Lesson: 1d1:16
- Lesson: 1e5:39
- Lesson: 2a3:52
- Lesson: 2b2:20
- Lesson: 2c2:29
- Lesson: 2d3:09
- Lesson: 2e3:23

In this lesson, we will learn how to turn a linear system into a matrix. What we do is draw a big bracket, take all the coefficients of each term and write it in, draw a vertical line, write all the numbers after the equal sign, and end it with another big bracket. Terms that do not seem to have a coefficient actually do. For example the term y can be rewritten to 1*y, and so the coefficient of this will be 1. Notice that when you turn it into a matrix, all the variables disappear since the most important part are the numbers.

Basic Concepts: Notation of matrices

We can represent a linear system as a matrix. For example, the linear system

$1x+2y+3z=4$
$5x+6y+7z=8$
$9x+10y+11z=12$

can be represented as the matrix:

where $x,y,z$ are variables and the vertical line represents the equal sign for each linear equation. We see all the $x,y,z$'s disappear, and we take all the coefficients and the numbers after the equal sign.

can be represented as the matrix:

where $x,y,z$ are variables and the vertical line represents the equal sign for each linear equation. We see all the $x,y,z$'s disappear, and we take all the coefficients and the numbers after the equal sign.

- IntroductionRepresenting a linear system as a matrix Overview:

- 1.
**Representing a linear system as a matrix**

Represent each linear system as a matrix:a)$x+6y-3z=3$

$4x+2y-z=10$

$6x+10y+20z=0$b)$-3x+7y=10$

$10x+2y=15$c)$v+w+x+y+z=0$

$x+y+z=5$

$x+y=3$

$2v+4w=2$

$y=3$d)$9x=3$e)$2w+6y+2z=3$

$3x+6y=2$

$x+y+z=10$

$w+2x+10y+z=7$ - 2.
**Representing a matrix as a linear system**

Represent each matrix as a linear system:a)b)c)d)e)

1.

Linear Equations with Matrices

1.1

Notation of matrices

1.2

Solving systems of linear equations by graphing

1.3

Representing linear system as a matrix

1.4

The three types of matrix row operations

1.5

Solving a linear system with matrices using Gaussian elimination

1.6

Row reduction and echelon forms

1.7

Linear combination and vector equations in $R^n$

1.8

Matrix equation Ax=b

1.9

Solution sets of linear systems

1.10

Application of linear systems

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