8.(i) 14 (ii) − 6 (iii) − 18 (iv) 4
(v) 0 (vi) 1- (i) 3
∣
∣∣
∣12
− 12∣
∣∣
∣+∣
∣∣
∣02
42∣
∣∣
∣+^2∣
∣∣
∣01
4 − 1∣
∣∣
∣(ii) − 0∣
∣
∣
∣− 12
− 12∣
∣
∣
∣+^1∣
∣
∣
∣32
42∣
∣
∣
∣−^2∣
∣
∣
∣3 − 1
4 − 1∣
∣
∣
∣(iii) 2∣
∣
∣
∣01
4 − 1∣
∣
∣
∣−^2∣
∣
∣
∣3 − 1
4 − 1∣
∣
∣
∣+^2∣
∣
∣
∣3 − 1
01∣
∣
∣
∣(iv) 4∣∣
∣
∣− 12
12∣∣
∣
∣+^1∣∣
∣
∣32
02∣∣
∣
∣+^2∣∣
∣
∣3 − 1
01∣∣
∣
∣All equal to− 4- (i)
[
4 / 5 − 3 / 5
− 1 / 52 / 5]
(ii)1
18[ 1 − 57
71 − 5
− 571](iii)1
14[ 3 − 15
53 − 1
− 153]
(iv)1
5[− 10 4 9
15 − 4 − 14
−51 6](v)1
26[ 612 − 8
10 − 64
− 2 − 47]11.(i) No solution (ii) x=1,y=−3,z= 2 (iii) x=1,y=2,z= 3
12.x=1or4
- (i) x=1,y= 0 (ii) x=
3
62,y=−29
124(iii) x=1
2,y=2,z=−3
2
(iv) No solution- (i) Trivial solution only (ii) Non-trivial solution
(iii) Trivial solution only (iv) Non-trivial solution
(v) Non-trivial solution (vi) Trivial solution only15.Example:
x+y+z= 0
x+ 2 y+ 3 z= 0
2 x+ 3 y+ 4 z= 0
- (i) 1, 2 (ii) 3, 4 (iii) 1,−1(iv)4,6
(v) 0, 1, 2 (vi) 1 (twice) (vii) 1, 2, 3 (viii) 1,−2, 3
(ix) 1, 1± 2 j