6. By taking a= 2/5and b= -3/10verify, the following:
(i) la+b|<|a|+|b| (ii) |ab| = lal.|b|
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Answer:
Given : A=
⎣
⎢
⎢
⎡
−2
4
5
⎦
⎥
⎥
⎤
and B=[
1
3
−6
]
⟹A
′
=[
−2
4
5
] and B
′
=
⎣
⎢
⎢
⎡
1
3
−6
⎦
⎥
⎥
⎤
Consider B
′
A
′
=
⎣
⎢
⎢
⎡
1
3
−6
⎦
⎥
⎥
⎤
[
−2
4
5
]=
⎣
⎢
⎢
⎡
−2
−6
12
4
12
−24
5
15
−30
⎦
⎥
⎥
⎤
Consider AB=
⎣
⎢
⎢
⎡
−2
4
5
⎦
⎥
⎥
⎤
[
1
3
−6
]
=
⎣
⎢
⎢
⎡
−2
4
5
−6
12
15
12
−24
−30
⎦
⎥
⎥
⎤
⟹(AB)
′
=
⎣
⎢
⎢
⎡
−2
−6
12
4
12
−24
5
15
−30
⎦
⎥
⎥
⎤
=B
′
A
′
Hence, (AB)
′
=B
′
A
′
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