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Get Started Now- Intro Lesson6:27
- Lesson: 1a2:06
- Lesson: 1b1:50
- Lesson: 1c2:05
- Lesson: 1d1:29
- Lesson: 1e1:38
- Lesson: 1f1:31
- Lesson: 1g1:24
- Lesson: 2a1:13
- Lesson: 2b1:09
- Lesson: 2c1:01
- Lesson: 2d1:16
- Lesson: 2e2:46
- Lesson: 2f1:36
- Lesson: 2g1:29
- Lesson: 2h1:30
- Lesson: 2i1:26
- Lesson: 2j2:06

In this section, we will be learning about the dimensions of a matrix, as well as finding the matrix element within a matrix. Dimensions of a matrix are determined by the number of rows and columns in the matrix. We generally write the dimensions to be (# of rows) x (# of columns). A matrix element is an entry in the matrix. If you see the subscript of the letter, then that subscript will tell you which entry we are talking about in the matrix. For example, if the subscript is (4,6), then we are looking for the entry in the 4th row and 6th column.

A **matrix** is a list of numbers put in a rectangular bracket.

The **dimensions** of a matrix are the number of rows and columns of the matrix. For example, if the matrix has *m* rows and *n* columns, then we say that the dimensions matrix is *m* by *n*.

Each entry in the matrix is called a **matrix element**. Let the matrix be called *A*. Then we say that the matrix element $a_{4,6}$ is the entry in the 4th row and 6th column.

- IntroductionNotation of Matrices Overview:a)What is a matrix and the dimension of a matrix?b)Matrix elements
- 1.
**The Dimensions of a Matrix**

Determine the dimensions of the following matrices:

a)b)c)d)e)f)g) - 2.
**Matrix Elements**

Find the matrix element (or value) of the following matrix

a)$a_{1,1}$b)$a_{2,3}$c)$a_{4,6}$d)$a_{4,9}$e)$\frac{a_{2,5}}{a_{4,9}}$f)$2(a_{3,7})$g)$(a_{2,4})^2$h)$2(a_{4,2})+5$i)$\frac{a_{1,9}}{3}$j)$a_{3,5}+a_{1,1}$

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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