Transcript 8.2 Operations with Matrices

8.2 Operations With Matrices
Two matrices are equal if they have the same order.
Matrices must be equal (of the same order) to be able to add
them. For the matrices...
2
0 0
1 2 4
A   3 0 1 & B  1  4 3
1 3 2
2 1 2
1 6 12
Find 3A - B
  10 4  6
7 0 4
Solve for X in the equation
1 2
A
0 3
3X + A = B, where
3 4
B
2 1
First, solve the equation for X.
1
X  ( B A)
3
1 2
1 3 4
X  

0 3
3 2 1
1 4 6

3 2 2



4

3

2
3
2
2

3
To find the product of two matrices, we need to do row-bycolumn multiplication and then add the results.
For the product of two matrices to be defined, the number
of columns of the first matrix must equal the number of
rows of the second matrix.
A
m x n
B
n x p
equal
order of AB
=
AB
m x p
Example of Matrix Multiplication
1 0
3
2 1  2
2 4 2
1 0 0 
1 1 1
2 x 3
3 x 3
What is the resulting
matrix?
Are these the
same?
Start by multiplying row 1 by column 1.
1(-2) + 0(1) + 3(-1) = -5
2 x 3
Now multiply R1 by C2 . Then R1 by C3 .
7
-1
Now multiply R2 by C1 , C2 , and C3 .
What is the resulting matrix?
 5 7 1
3 6 6
Assignment: 1 - 9 odd, 11-27 odd