Matrix Algebra

Section 7.2

Review of order of matrices

526

3742 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 thatsolve for x and y

x² = 25

x = 5, -5

025

251

032

1 2

y

x

2y + 3 = 25

2y = 22

y = 11

Solve for each variable

52

81

5

3 z

yx

yx

8 yx 2 yx 13 z

•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 + BA + B =

Find A – BA – B =

375

216

380

086

321

542

B

A

3111

517

842

3151

135

2122

375

216

380

086

321

542

375

216

380

086

321

542

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

01612

642

1084

2A

375

216

380

086

321

542

B

A

6224

1411

1202

086

321

542

61410

4212

6160

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

7541

32

BA

BA =

7541

32

BA

BA = 433

5(2) + 7(-1) = 10 – 7 = 3

5(3) + 7(4) = 15 + 28 = 43

Find AB

375

216

380

086

321

542

BA