8.2 operations with matrices two matrices are equal if they have the same order. & find 3a - b...

8.2 Operations With Matrices

Two matrices are equal if they have the same order.

212

103

421

−−=A &

231

341

002

−−=B

Find 3A - B

407

6410

1261

−−=

Matrices must be equal (of the same order) to be able to addthem. For the matrices...

Solve for X in the equation 3X + A = B, where

30

21 −=A

12

43−=B

First, solve the equation for X. )(3

1ABX −=

⎟⎟⎠

⎞⎜⎜⎝

⎛ −−

−=

30

21

12

43

3

1X

22

64

3

1

−−

=3

2

3

2

23

4

−

−=

To find the product of two matrices, we need to do row-by-column multiplication and then add the results.

For the product of two matrices to be defined, the numberof columns of the first matrix must equal the number of rows of the second matrix.

A B = AB m x n n x p m x p

equal

order of AB

Example of Matrix Multiplication

=−−

−

−−111

001

242

212

301

2 x 3 3 x 3

Are these the same?

What is the resultingmatrix?

2 x 3

Start by multiplying row 1 by column 1.

1(-2) + 0(1) + 3(-1) = -5

Now multiply R1 by C2 . Then R1 by C3 .

7 -1

Now multiply R2 by C1 , C2 , and C3 .

What is the resulting matrix?

663

175

−−−

Assignment: 1 - 9 odd, 11-27 odd