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Byju's Answer
Standard XII
Mathematics
Hermitian Matrix
If A=[ai j] i...
Question
If A = [a
ij
] is a 3 × 3 scalar matrix such that a
11
= 2, then write the value of |A|.
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Solution
A scalar matrix is a diagonal matrix, in which all the diagonal elements are equal to a given scalar number.
Given
:
A
=
a
i
j
is
3
×
3
matrix
,
where
a
11
=
2
⇒
A
=
2
0
0
0
2
0
0
0
2
⇒
A
=
2
0
0
0
2
0
0
0
2
=
2
×
2
0
0
2
Expanding
along
C
1
=
2
×
2
×
2
=
8
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Similar questions
Q.
If
A
=
a
i
j
is a 3 × 3 diagonal matrix such that a
11
= 1, a
22
= 2 a
33
= 3, then find |A|.
Q.
If
A
=
[
a
i
j
]
is scalar matrix of order
n
×
n
such that
a
i
j
=
k
for all
i
, then
|
A
|
equals
Q.
Let
A
be a
3
×
3
matrix such that
a
11
=
a
33
=
2
and all the other
a
i
j
=
1
. Let
A
−
1
=
x
A
2
+
y
A
+
z
I
, then the value of
(
x
+
y
+
z
)
where
I
is a unit matrix of order
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, is-
Q.
Let
A
be a
3
×
3
matrix such that
a
11
=
a
33
=
2
and all the other
a
i
j
=
1
. Let
A
−
1
=
x
A
2
+
y
A
−
z
I
, then find the value of
(
x
+
y
+
z
)
where
I
is a unit of matrix of order 3.
Q.
If
A
=
[
a
i
j
]
is a scalar matrix of order
n
×
n
such that
a
i
j
=
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for all then trace of
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