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