# Matrices

Definition: A matrix is a rectangular array of numbers. It has dimensions written as m x n where it is m rows and n columns. Matrices can be used to solve systems of equations.

Matrices can be added or subtracted from one another if they have the same dimensions.
Matrices can be multiplied by a single scalar value. Every entry within the matrix is multiplied by the scalar. Matrices can be multiplied by one another if the first matrix has the same number of columns as the second matrix has of rows. In order for matrix A to be multiplied by matrix B, matrix A must have m x n dimensions, and matrix B must have n x o dimensions.

Example: Multiply the matrices.

Solution:

Step 1: To find each entry, we must multiply and add.

Step 2: To find the entry for row 1, column 1, we must multiply the first row of the first matrix with the first column of the second matrix. (1*0 + 0*2 + 1*1) = 1.

Step 3: To find the entry for row 1, column 2, we must multiply the first row of the first matrix by the second column of the second matrix. (1*1 + 0*2 + 1*1) = 2.

Step 4: To find the entry for row 2, column 1, we multiply the second row with the first column. (0*0 + 2*2 + 3*1)= 7

Step 5: To find the entry for row 2, column 2, we multiply the second row with the second column. (0*1 + 2*2 + 3*1) = 7.