Matrix Algebra Section 7.2

Review of order of matrices 2 rows, 3 columns Order is determined by: (# of rows) x (# of columns)

Equality of Matrices A = B Two Matrices A and B are equal if and only if both of the following are true 1. A and B have the same order m x n 2. Every pair of corresponding elements are equal

Given that solve for x and y x² = 25 x = 5, -5 2y + 3 = 25 2y = 22 y = 11

Solve for each variable

If A is an m x n matrix and B is an m x n, then you may add or subtract the corresponding elements in matrix A and matrix B. When adding or subtracting matrices, their orders must be the same. To add and subtract matrices, simply add or subtract each corresponding element. Matrix Addition and Subtraction

Find A + B A + B = Find A – B A – B =

Multiplying by a Scalar Order does not matter Simply multiply each element in the matrix by the number (scalar) out front

Multiply a Matrix by a scalar Find 2A Find -2B + A

Multiply Matrices The number of columns in the first matrix must be equal to the number of rows in the second matrix. You can multiply a 2 x 3 matrix by a 3 x 5 matrix You can NOT multiply a 2 x 3 matrix by a 2 x 3 matrix

Find AB Order of matrix A is 2 x 2 Order of matrix B is 1 x 2 (2 x 2)(1 x 2) We CAN’T find AB Find BA (1 x 2)(2 x 2) CAN Multiply Resulting Matrix is 1 x 2

BA = 5(2) + 7(-1) = 10 – 7 = 3 5(3) + 7(4) = = 43

Find AB