C: ANSWERS TO SELECTED PROBLEMS
Chapter
6.1, Systems of Linear Equations in Two Variables
1. Yes, it is a
solution. 3. 
5. No solutions,
inconsistent, independent. 7. 
9. 
11. 
13. No, it is not a
solution. 15. No solution,
inconsistent, independent.
17. No solution,
inconsistent, independent. 19. (2,3) consistent
and independent.
21. 
23. 
25. 
27. 
29. 
Chapter 6.2, Matrices and
Systems of Linear Equations
1. 
. 3. 
5. (Ð1,2,3). 7. No solution, the
system is inconsistent.
9. (Ð3,2). 11. (7,3).
13. 
15. (Ð2,Ð1,4).
17. 
19. No solution.
21. 
23. No solution.
25. 
27. 
29. 
Chapter
6.3, Matrix Notation, Algebra, and Inverses
1. A 2x2, B
2x5, C 3x1, D 1x2, E
2x2. 3. 
5. 
7. 
9. 
11. 
13. 
15. [a] E, [b] 
, [c] 
. 17. [a] Not possible.
[b] A, [c] 
.
19. [a]
, [b]
, [c]
. 21. 
23. 
25. 
27. 
29. [a]
, [b]
, [c]
31. 
33. 
35. 
Chapter 6.4, The Leontief Input-Output Model
1. [a] 
, [b] 
, [c] 
, [d] 
.
3. [a] 
, [b] 
, [c] 
, [d] 
,
[e]
, [f] 5896.9
work-days.
5. [a] 
, [b] 
, [c] 
, [d] 
,
[e]
, [f] 2.213 K$.
7. [a] 
; 
; 
.
9. [a] 
; 
; 
.
Chapter 6.5, Chapter Review
1. (-4,-8);
Consistent; Independent. 3. No solution.
5. (0,0,0); Consistent; Independent. 7. $1600 at 10%,
$3400 at 10.5%.
9. 74.5, 68.5, 82. 11. (1,2).
13. 
15. 
. 17. 
.
19. Not possible. 21. 
.
23. 
. 25. 
.
27. 
29. $10,000 at 12%,
$12,000 at 13%, $18,000 at 14.5%.