College Algebra 9th txtbk

SECTION 7–4 Solving Systems of Linear Equations Using Matrix Inverse Methods 483
Z Figure 4 Z Figure 5
Writing the numbers in the columns of this matrix in sequence and using the correspondence
between numbers and letters noted earlier produces the decoded message:
23 8 15 27 9 19 27 11 1 18 12 27 7 1 21 19 19 27
W H O I S K A R L G A U S S
The answer to this question can be found somewhere in this chapter.
MATCHED PROBLEM 8
The message
46 84 85 55 101 100 59 95 132 25 42 53 52 91 90 43 71 83 19 37 25
was encoded with the matrix A shown here. Decode this message.
1 1 1
A £ 2 1 2§
2 3 1
ANSWERS TO MATCHED PROBLEMS
3 1 1 1 0 0
1. (A) £ 1 1 0 † 0 1 0§
(B)
1 0 1 0 0 1
1 1 1 3 1 1 1 0 0
(C) £ 1 2 1 §£ 1 1 0§ £ 0 1 0§
1 1 2 1 0 1 0 0 1
2. c 1 3 3. Does not exit
1 d
1 2
1 0 0
£ 0 1 0 †
0 0 1
1 1 1
1 2 1 §
1 1 2
4.
AX C B
(AX C ) C B C
AX (C C ) B C
AX 0 B C
AX B C
A 1 (AX ) A 1 (B C )
(A 1 A) X A 1 (B C )
IX A 1 (B C )
X A 1 (B C )
5. x 1 2, x 2 5, x 3 0
6. (A) x 1 2, x 2 5, x 3 4 (B) x 1 0, x 2 1, x 3 4
7. A 1 2.25 25
c
Client 1: $15,000 in A and $5,000 in B; Client 2: $18,750 in A and
1.25 25 d ;
$31,250 in B; Client 3: $10,000 in A
8. WHO IS WILHELM JORDAN