12. If a -
3
and b
2
4
5
verify that
(1) lax b] =1dxb
(ii) la-bla-
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Answer:
Answer
Given:A=
⎣
⎢
⎢
⎡
−1
2
3
⎦
⎥
⎥
⎤
B=[
−2
−1
−4
]
AB=
⎣
⎢
⎢
⎡
−1
2
3
⎦
⎥
⎥
⎤
[
−2
−1
−4
]=
⎣
⎢
⎢
⎡
2
−4
−6
1
−2
−3
4
−8
−12
⎦
⎥
⎥
⎤
Now, AB
T
=
⎣
⎢
⎢
⎡
2
1
4
−4
−2
−8
−6
−3
−12
⎦
⎥
⎥
⎤
−(i)
B
T
=
⎣
⎢
⎢
⎡
−2
−1
−4
⎦
⎥
⎥
⎤
;A
T
=[
−1
2
3
]
B
T
A
T
=
⎣
⎢
⎢
⎡
−2
−1
−4
⎦
⎥
⎥
⎤
[
−1
2
3
]=
⎣
⎢
⎢
⎡
2
1
4
−4
−2
−8
−6
−3
−12
⎦
⎥
⎥
⎤
−(ii)
We can say that (i)=(ii)
hence (AB)
T
=B
T
A
T
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