MATRICES MATRIX OPERATIONS

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.

Special Matrices Some matrices have special names because of what they look like. a)Row matrix: only has 1 row. b)Column matrix: only has 1 column. c)Square matrix: has the same number of rows and columns. d)Zero matrix: contains all zeros.

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

Matrix Addition/Subtraction  You can add or subtract matrices only if they have the same dimensions.  To do this, you add or subtract the corresponding elements (numbers in the same positions).

Example #1:

Example #2: NOT POSSIBLE! The matrices do not have the same dimensions so they cannot be added together.

Scalar Multiplication  Multiplying a matrix by one number, called a scalar.  To do this, multiply each entry in the matrix by the number outside. Just like distributing!!

Example #3:

Example #4: Simplify:

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.

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

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

Set each element equal and solve!