College Algebra 9th txtbk

SECTION 7–3 Matrix Operations 463
2
2
2 3
3
1
1
2
1
2
1
3 2
3
0
2
2 3 1
1
1
2 3 1
2 1
1
2
2
1
2 1 2
3
0
2
3
0
2
(2)(1) (3)(2) (1)(1) (2)(3) (3)(0) (1)(2)
(2)(1) (1)(2) (2)(1) (2)(3) (1)(0) (2)(2)
9
2
2 2
4
2
EXAMPLE 8 Matrix Multiplication
Given
A £ 1 0§
2 1
1 2
B c 1 1 0 1
2 1 2 0 d
C c 2 6
1 3 d
D c 1 2
3 6 d
Find each product that is defined:
(A) AB (B) BA (C) CD (D) DC
SOLUTIONS
3 2
2 4
2 1
(A) AB £ 1 0§ c 1 1 0 1
2 1 2 0 d
1 2
(2)(1) (1)(2) (2)(1) (1)(1) (2)(0) (1)(2) (2)(1) (1)(0)
£ (1)(1) (0)(2) (1)(1) (0)(1) (1)(0) (0)(2) (1)(1) (0)(0) §
(1)(1) (2)(2) (1)(1) (2)(1) (1)(0) (2)(2) (1)(1) (2)(0)
3 4
4 1 2 2
£ 1 1 0 1§
3 3 4 1
2 4
3 2
(B) BA c 1 1 0 1 2 1
2 1 2 0 d£ 1 0§
1 2
Product is not defined.
(C)
2 2 2 2
CD c 2 6
1 3 dc1 2
3 6 d
(2)(1) (6)(3) (2)(2) (6)(6)
c
(1)(1) (3)(3) (1)(2) (3)(6) d
2 2
20 40
c
10 20 d