1. 4.1 Introduction to Matrices

2. About Matrices
A matrix is a rectangular arrangement of numbers in rows and columns. Rows run horizontally and columns run vertically.
The dimensions, or size, of a matrix are:
# of rows X # of columns.

3. Special Matrices
Some matrices have special names because of what they look like.
Row matrix: only has 1 row.
Column matrix: only has 1 column.
Square matrix: has the same number of rows and columns.
Zero matrix: contains all zeros.
Identity matrix: 1’s going down the main diagonal and zeros everywhere else

4. Dimensions: 4x1 COLUMN MATRIX Dimensions: 3x2
Find the dimensions of each matrix.
Dimensions: 4x1 COLUMN MATRIX
Dimensions: 3x2
Dimensions: 2x4

5. Using Matrices to Solve Equations
Equal Matrices - two matrices that have the same dimensions and each element of one matrix is equal to the corresponding element of the other matrix.
*The definition of equal matrices can be used to find values when elements of the matrices are algebraic expressions.

6. Examples: Find the values for x and y
* Since the matrices are equal, the corresponding elements are equal!
Step 1: Form two linear equations.
Step 2: Solve the system using any method.

7. Plug y in to get x.
Now check your answer:

8. Set each element equal and solve!