College Algebra 9th txtbk

SECTION 7–3 Matrix Operations 459
SOLUTION
c 3 2
5 0 d c 2 2 3 (2) 2 2
d c
3 4 5 3 0 4 d c 5 4
2 4 d
MATCHED PROBLEM 2 Subtract: [2 3 5] [3 2 1]
EXAMPLE 3 Matrix Equations
Find a, b, c, and d so that
c a b
c d d c 2 1
5 6 d c 4 3
2 4 d
SOLUTION
c a b
c d d c 2 1
5 6 d c 4 3
2 4 d
c a 2 b (1) 4 3
d c
c (5) d 6 2 4 d
c a 2 b 1
c 5 d 6 d c 4 3
2 4 d
Subtract the matrices on the left side.
Simplify.
Set corresponding elements equal to each other.
a 2 4 b 1 3 c 5 2 d 6 4
a 6 b 2 c 7 d 10
MATCHED PROBLEM 3
Find a, b, c, and d so that
c a b
c d d c 4 2
1 3 d c 2 5
8 2 d
Z Multiplying a Matrix by a Number
The product of a number k and a matrix M, denoted by kM, is a matrix formed by multiplying
each element of M by k.
EXAMPLE 4 Multiplying a Matrix by a Number
3 1 0
Multiply: 2 £ 2 1 3§
0 1 2
SOLUTION
MATCHED PROBLEM 4
3 1 0 6 2 0
2 £ 2 1 3§ £ 4 2 6 §
0 1 2 0 2 4
1.3
Multiply: 10 £ 0.2 §
3.5