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Byju's Answer
Standard X
Mathematics
Polynomial
Let A=[ai j] ...
Question
Let A = [a
ij
] and B = [b
ij
] be a square matrices of order 3 such that b
i
1
= 2 a
i
1
, b
i
2
= 3 a
i
2
and b
i
3
= 4 a
i
3
, i = 1, 2, 3
If |A| = 5, then |B| = _____________.
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Solution
Given:
A and B are square matrices of order 3
b
i
1
= 2 a
i
1
, b
i
2
= 3 a
i
2
and b
i
3
= 4 a
i
3
, i = 1, 2, 3
|A| = 5
Let
A
=
a
11
a
12
a
13
a
21
a
22
a
23
a
31
a
32
a
33
Since
,
b
i
1
=
2
a
i
1
,
b
i
2
=
3
a
i
2
and
b
i
3
=
4
a
i
3
Therefore
,
b
11
=
2
a
11
,
b
21
=
2
a
21
,
b
31
=
2
a
31
,
b
12
=
3
a
12
,
b
22
=
3
a
22
,
b
32
=
3
a
32
,
b
13
=
4
a
13
,
b
23
=
4
a
23
,
b
33
=
4
a
33
B
=
b
11
b
12
b
13
b
21
b
22
b
23
b
31
b
32
b
33
⇒
B
=
2
a
11
3
a
12
4
a
13
2
a
21
3
a
22
4
a
23
2
a
31
3
a
32
4
a
33
Taking
out
2
,
3
and
4
common
from
C
1
,
C
2
and
C
3
,
respectively
⇒
B
=
2
×
3
×
4
a
11
a
12
a
13
a
21
a
22
a
23
a
31
a
32
a
33
⇒
B
=
24
A
⇒
B
=
24
×
5
∵
A
=
5
⇒
B
=
120
Hence, |B| =
120
.
Suggest Corrections
1
Similar questions
Q.
Let
A
=
[
a
i
j
]
and
B
=
[
b
i
j
]
be two
3
×
3
real matrices such that
b
i
j
=
(
3
)
(
i
+
j
−
2
)
a
j
i
, where
i
,
j
=
1
,
2
,
3
. If the determinant of
B
is
81
, then the determinant of
A
is :
Q.
Let
A
=
[
a
i
j
]
and
B
=
[
b
i
j
]
be two
3
×
3
real matrices such that
b
i
j
=
(
3
)
(
i
+
j
−
2
)
a
j
i
, where
i
,
j
=
1
,
2
,
3
. If the determinant of
B
is
81
, then the determinant of
A
is :
Q.
If
two
matrices
A
and
B
are
such
that
−
[
A
ij
]
m
×
n
=
[
Bij
]
p
×
q
then
,
m
=
p
,
n
=
q
and
A
ij
=
Bij
for
all
i
and
j
Q.
Let
A
=
[
a
i
j
]
be a square matrix of order
n
such that
a
i
j
=
{
0
i
f
i
≠
j
i
i
f
i
=
j
Statement - 1 : The inverse of A is matrix
B
=
[
b
i
j
]
such that
b
i
j
=
{
0
i
f
i
≠
j
1
i
i
f
i
=
j
Statement - 2 : The inverse of a diagonal matrix is a scalar matrix.
Q.
let
A
=
[
a
i
j
]
3
×
3
and
B
=
[
a
i
j
]
3
×
3
, where
b
i
j
=
2
i
+
j
a
i
j
for all
i
,
j
. if
i
,
j
.
If
|
A
|
=
2
, then
|
B
|
=
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