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Byju's Answer
Standard XII
Mathematics
Diagonal Matrix
Define a diag...
Question
Define a diagonal matrix.
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Solution
A diagonal matrix is the type of matrix which has non zero elements present in the diagonal. In other words, all other elements other than diagonal elements must be 0.
An Example of diagonal matrix is given by:
1
0
0
0
3
0
0
0
4
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Similar questions
Q.
Let A be a
2
×
2
matrix with non-zero entries and let
A
2
=
I
, where I is
2
×
2
identity matrix. Define Tr(A)
=
sum of diagonal elements of A and
|
A
|
=
determinant of matrix A.
Statement-1 Tr(A)
=
0
Statement-2:
|
A
|
=
1
Q.
Assertion :The matrix
⎡
⎢
⎣
a
0
0
0
0
b
0
0
0
0
c
0
⎤
⎥
⎦
is a diagonal matrix Reason:
A
[
a
i
j
]
is a square matrix such that
a
i
j
=
0
for all
i
≠
j
, then
A
is called diagonal matrix.
Q.
The matrix
A
=
1
0
0
0
2
0
0
0
4
is
(a) identity matrix
(b) symmetric matrix
(c) skew-symmetric matrix
(d) diagonal matrix
Q.
Assertion :The matrix
⎡
⎢
⎣
1
0
0
0
0
2
0
0
0
0
3
0
⎤
⎥
⎦
is a diagonal matrix Reason:
A
=
(
a
i
j
)
m
×
m
is a square matrix such that entry
a
i
j
=
0
∀
i
≠
j
,
then A is called diagonal matrix.
Q.
Diagonal matrix is also a triangular matrix how ? And what is triangular matrix...?
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