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Byju's Answer
Standard XII
Mathematics
Summation by Sigma Method
If A is an ...
Question
If
A
is an idempotent matrix satisfying,
(
I
−
0.4
A
)
−
1
=
I
−
α
A
, where
I
is the unit matrix of the same order as that of
A
, then the value of
|
9
α
|
is equal to ..............
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Solution
A
i
s
a
n
i
d
e
m
p
o
t
e
n
t
m
a
t
r
i
x
i
.
e
A
2
=
A
(
I
−
0.4
A
)
−
1
=
I
−
α
A
⇒
I
=
(
I
−
α
A
)
(
I
−
0.4
A
)
=
I
2
−
0.4
A
I
−
α
A
I
+
0.4
α
A
2
=
I
+
A
(
−
0.4
−
0.6
α
)
⇒
α
=
−
4
6
H
e
n
c
e
|
9
α
|
=
6
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Similar questions
Q.
If A is an idempotent matrix satisfying
(
I
−
0.4
A
)
−
1
=
I
−
α
A
where I is the unit matrix of the same order as that of A then the value of
α
is equal to
Q.
For a matrix A, if
A
2
=
I
where I is a unit matrix of same order, then (I - A)(I + A) is
Q.
If
Z
is an idempotent matrix, then
(
I
+
Z
)
n
is equal to
Q.
Let
A
be a nilpotent matrix of index
m
.
If
(
I
−
A
)
n
=
I
+
A
+
A
2
+
⋯
+
A
m
−
1
,
where
I
is the identity matrix of order same as matrix
A
,
then the value of
n
is
Q.
If
A
is a non-singular matrix such that
(
A
−
2
I
)
(
A
−
4
I
)
=
O
, where
I
is an identity matrix of the same order as that of
A
. Then
1
6
A
+
4
3
A
−
1
is equal to:
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