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Byju's Answer
Standard XII
Mathematics
Rank of a Matrix
If A=[ 1 2 ...
Question
If
A
=
⎡
⎢
⎣
1
2
1
−
1
0
2
0
1
−
1
⎤
⎥
⎦
, find the rank of
A
.
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Solution
|
A
|
=
∣
∣ ∣
∣
1
2
1
−
1
0
2
0
1
−
1
∣
∣ ∣
∣
Expand along first column,
=
1
(
0
−
2
)
+
1
(
−
2
−
1
)
=
−
2
−
3
=
−
5
≠
0
Since determinant of matrix
A
is non-zero and order of matrix is
3
So the rank of the matrix is
3
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Similar questions
Q.
The reciprocal matrix of
⎡
⎢
⎣
1
0
2
0
1
−
1
1
2
1
⎤
⎥
⎦
is
Q.
If
⎡
⎢
⎣
4
1
3
⎤
⎥
⎦
A =
⎡
⎢
⎣
−
1
8
4
−
1
2
1
−
3
6
3
⎤
⎥
⎦
Find A
Q.
If
⎡
⎢
⎣
4
1
3
⎤
⎥
⎦
A
=
⎡
⎢
⎣
−
4
8
4
−
1
2
1
−
3
6
3
⎤
⎥
⎦
, find
A
. If
A
=
[
a
,
b
,
c
]
, find the value of
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+
b
+
c
.
Q.
If all letters of the word 'RANK' are arranged in all possible manner as they are in a dictionary, then find the rank of the word 'RANK'.
Q.
Find the value of
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Rank of a Matrix
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