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Byju's Answer
Standard XII
Physics
Multiplication with Vectors
If A=[ -1 ...
Question
If
A
=
⎡
⎢
⎣
−
1
5
−
2
2
7
1
3
9
1
⎤
⎥
⎦
and
B
=
⎡
⎢
⎣
−
4
1
1
1
2
3
−
5
0
1
⎤
⎥
⎦
, then verify that
(
i
)
(
A
+
B
)
T
=
A
T
+
B
T
(
i
i
)
(
A
−
B
)
T
=
A
T
−
B
T
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Solution
We have:
A
T
=
⎡
⎢
⎣
−
1
5
−
2
2
7
1
3
9
1
⎤
⎥
⎦
B
T
=
⎡
⎢
⎣
−
4
1
1
1
2
3
−
5
0
1
⎤
⎥
⎦
(i)
A
+
B
=
⎡
⎢
⎣
−
1
5
−
2
2
7
1
3
9
1
⎤
⎥
⎦
+
⎡
⎢
⎣
−
4
1
1
1
2
3
−
5
0
1
⎤
⎥
⎦
∴
(
A
+
B
)
=
⎡
⎢
⎣
−
5
3
−
2
6
9
9
−
1
4
2
⎤
⎥
⎦
A
T
+
B
T
=
⎡
⎢
⎣
−
1
2
3
5
7
9
−
2
1
1
⎤
⎥
⎦
+
⎡
⎢
⎣
−
4
1
−
5
1
2
0
1
3
1
⎤
⎥
⎦
=
⎡
⎢
⎣
−
5
6
−
1
3
9
4
−
2
9
2
⎤
⎥
⎦
Hence, we have verified that
(
A
+
B
)
T
=
A
T
+
B
T
(ii)
A
−
B
=
⎡
⎢
⎣
−
1
5
−
2
2
7
1
3
9
1
⎤
⎥
⎦
−
⎡
⎢
⎣
−
4
1
1
1
2
3
−
5
0
1
⎤
⎥
⎦
∴
(
A
−
B
)
T
=
⎡
⎢
⎣
3
1
8
4
5
9
−
3
−
2
0
⎤
⎥
⎦
A
T
−
B
T
=
⎡
⎢
⎣
−
1
5
−
2
2
7
1
3
9
1
⎤
⎥
⎦
−
⎡
⎢
⎣
−
4
1
1
1
2
3
−
5
0
1
⎤
⎥
⎦
=
⎡
⎢
⎣
3
1
8
4
5
9
−
3
−
2
0
⎤
⎥
⎦
Hence, we have proved that
(
A
−
B
)
T
=
A
T
−
B
T
.
Suggest Corrections
0
Similar questions
Q.
Let
A
=
1
-
1
0
2
1
3
1
2
1
and
B
=
1
2
3
2
1
3
0
1
1
.
Find A
T
, B
T
and verify that
(i) (A + B)
T
= A
T
+ B
T
(ii) (AB)
T
= B
T
A
T
(iii) (2A)
T
= 2A
T
.
Q.
Let
A
=
2
-
3
-
7
5
and
B
=
1
0
2
-
4
, verify that
(i) (2A)
T
= 2A
T
(ii) (A + B)
T
= A
T
+ B
T
(iii) (A − B)
T
= A
T
− B
T
(iv) (AB)
T
= B
T
A
T
Q.
If
A
T
=
⎡
⎢
⎣
3
4
−
1
2
0
1
⎤
⎥
⎦
and
B
=
[
−
1
2
1
1
2
3
]
,
then find
A
T
−
B
T
Q.
If
A
T
=
⎡
⎢
⎣
3
4
−
1
2
0
1
⎤
⎥
⎦
and
B
=
[
−
1
2
1
1
2
3
]
, then find
A
T
−
B
T
.
Q.
I
f
2
A
+
B
T
=
[
2
−
3
4
7
]
and
A
T
−
B
=
[
4
−
5
0
1
]
,then
A
=
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