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Byju's Answer
Standard XII
Mathematics
Square Matrix
If begin bmat...
Question
If
[
a
+
2
b
2
c
−
d
c
+
4
d
4
b
−
a
]
=
[
10
2
37
14
]
, then the values of
a
,
b
,
c
,
d
respectively is
(
a
)
2
,
4
,
6
,
8
(
b
)
2
,
4
,
5
,
8
(
c
)
2
,
4
,
5
,
7
(
d
)
1
,
4
,
5
,
8
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Solution
[
a
+
2
b
2
c
−
d
c
+
4
d
4
b
−
a
]
=
[
10
2
37
14
]
By the equality of two matrices, equating the corresponding elements, we get
a
+
2
b
=
10
.
.
.
(
1
)
2
c
−
d
=
2
.
.
.
(
2
)
c
+
4
d
=
37
.
.
.
(
3
)
4
b
−
a
=
14
.
.
.
(
4
)
.
Adding eqn(1) and (4), we get
6
b
=
24
⇒
b
=
4
⇒
a
=
2
.
Multiplying eqn(2) by
4
and add eqn(3), we get
8
c
−
4
d
+
c
+
4
d
=
45
⇒
9
c
=
45
⇒
c
=
5
⇒
d
=
8
.
The values are
a
=
2
,
b
=
4
,
c
=
5
,
d
=
8
.
Ans :
(
b
)
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