082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

Review exercises 8 323
4 (a) −8
⎛
(b) ⎝
⎞
0 −80
0 −44⎠
−2 31
⎛ ⎞
0 8 0
1
(c) ⎝0 4 −4⎠
8
2 −3 −1
5
⎛
1
⎝
21
−7 6 −10
−14 3 −5
70 7
x=1,y=−1,z=2
⎞
⎠
6 x=2µ−λ,y=1+2λ−2µ,z=λ,w=µ
7 x = 0.082,y = 0.184,z = 0.082
8 x = 1.462,y = −0.308,z = −0.385
12 (a) x=1,y=−13
(b)x=1,y=1,z=2
13 (a),(c)and(d)have non-trivialsolutions.
14 (b)and(c)have non-trivialsolutions.
15 (a) λ 2 +λ−6=0
(b) ( λ=−3,2 ) ( ) 1 1
(c) ,
−3 −0.5
16 (a) λ=3
( ) 1
(b)
−1
17 (a) λ=2,3,4
⎛
(b) ⎝
⎞ ⎛ ⎞ ⎛ ⎞
1 1 0
1⎠,
⎝2⎠,
⎝1⎠
−1 1 1
10 (a) f(t) = 4 3 t − 1 3 t3
( ( −6 −6
11 (a) (b)
6)
6)
(c)
( ) −3µ
3µ