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(MATH113)math113_hw1_book.pdf
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Solution Set 1-Textbook Exercises
Ex 1.1
18. No.
5
22. h = .
3
28. ad . bc .
=0
Ex 1.2
16. (a) It is consistent and has unique solution.
(b) It is consistent and has in.nity solutions.
18. h .
= 15
24. No.
Ex 1.3
6.

10.


..
.2x1 +8x2 + x3 =0, 3x1 +5x2 . 6x3 =0
......
1 .7.
86 .5 15
22. Find it yourself.
26. (a) Yes.
(b) Trivial.
Ex 1.4 28.c1a1+c2a2+c3a3+c4a4+c5a5 = b where c1 = .3,c2 =2,c3 =4,c4 = .1,c5 =2 and
4 39
.
. + x2 . + x3
.
. =
..
1
.2
2
x1
a1 = .3 5 , a2 = 5 8 , a3 = .4 1 , a4 = 9 .2 , a5 = 7 .4 , b = 8 .1 .
36. Ignore it. 38. No.
Ex 1.5

12.
.
.......
x1 .5 .8 .1
.......
x2
x3
x4
x5
.......
=
.......
1
0
0
0
.......
u +
.......
0
7
1
0
.......
v +
.......
0
.4
0
1
.......
w
x6 000
28. No.
30. (a) Yes. (b)No.
Ex 1.7
16. Linear dependent.
30. (a) n
(b) It has only a trivial solution of equation Ax = 0.
1
32. (x1,x2,x3)=(t, 2t, .t)
34. True.
Ex 1.8
4. x =(..5, .3, 1). . .27
20. A = .
5 .3
26.T (su + tv)= sT (u)+ tT (v) =Span{T (u),T (v)} for all s, t.
case 1: If T (u) and T (v) are linearly independent, then it will map onto a plane
through 0.
case 2: If T (u) and T (v) are linearly dependent but not both are zero, then it will
map onto a line through 0.
case 3: If T (u) and T (v) are linearly dependent and both are zero, then it will map
onto origin.

Ex 1.9 .. 0 .1
8. T =
10
..
1 .2
..
16. .21
10
22. (x1,x2) = (5, 3)