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NDA Math Determinants
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© examsnet.com
Question : 54
Total: 68
If A is an invertible matrix of order n and k is any positive real numbers ,then the value of
[
d
e
t
(
K
A
)
]
−
1
det A is
[NDA II 2015]
k
−
n
k
−
1
k
n
n
k
Validate
Solution:
If A is matrix that is invertible then det - (kA) will be
k
n
.
det
(
A
)
where n is the order.
∴
[
d
e
t
(
K
A
)
]
−
1
d
e
t
(
A
)
=
[
(
K
)
n
×
d
e
t
(
A
)
]
−
1
⋅
d
e
t
(
A
)
=
K
−
n
×
1
d
e
t
(
A
)
×
d
e
t
(
A
)
=
K
−
n
© examsnet.com
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