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Byju's Answer
Standard XII
Mathematics
Rank of a Matrix
If A = [ 1 0 ...
Question
If
A
=
⎡
⎢
⎣
1
0
1
0
1
2
0
0
4
⎤
⎥
⎦
and
|
3
A
|
=
k
|
A
|
,
then
k
is
A
27.00
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B
27
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C
27.0
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Solution
A
=
⎡
⎢
⎣
1
0
1
0
1
2
0
0
4
⎤
⎥
⎦
⇒
|
A
|
=
4
3
A
=
⎡
⎢
⎣
3
0
3
0
3
6
0
0
12
⎤
⎥
⎦
Expanding along the first row
|
3
A
|
=
3
∣
∣
∣
3
6
0
12
∣
∣
∣
−
0
∣
∣
∣
0
6
0
12
∣
∣
∣
+
3
∣
∣
∣
0
3
0
0
∣
∣
∣
=
3
(
3
×
12
−
6
×
0
)
−
0
(
0
×
12
−
0
×
6
)
+
(
0
×
0
−
0
×
3
)
=
3
(
36
−
0
)
+
0
+
3
(
0
+
0
)
=
3
×
36
=
108
=
27
×
4
=
27
|
A
|
Hence
k
=
27
Suggest Corrections
0
Similar questions
Q.
If A=
⎡
⎢
⎣
1
0
1
0
1
2
0
0
4
⎤
⎥
⎦
then show that |3A|=27|A|
Q.
If A is a
3
×
3
matrix and |3A| = k |A|, then k =
Q.
If
A
is a
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3
matrix and
det
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)
=
k
(
det
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)
, then
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=
Q.
If
t
a
n
3
A
t
a
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A
=
k
, then prove that
s
i
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A
s
i
n
A
=
2
k
k
−
1
and that k cannot lie between
1
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and 3.
Q.
If
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A
|
=
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Rank of a Matrix
Standard XII Mathematics
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