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27.A square m...

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27.A square matrix of order n is both involuntary and idempotent matrix. The value of the determinant of (A+I) is equal to (where I is an identity matrix of order n)

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X

is any matrix of order

n \times p

n

p

are integers) and

l

is an identity matrix of order

n \times n

, then the matrix

M = I - X {(X^{'} X)}^{- 1} X^{'}

is
(i) Idempotent matrix
(ii)

M X = 0

Choose the correct answer

A

is an idempotent matrix satisfying,

(I - 0.4 A)^{- 1} = I - α A

I

is the unit matrix of the same order as that of

A

, then the value of

| 9 α |

is equal to ..............

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

Q. A square matrix P satisfies

P^{2} = I - P,

where I is an identity matrix of order as order of P. if

P^{n} = 5 I - 8 P, t h e n n =

Q. A matrix of order 3 × 3 has determinant 2. What is the value of |A (3I)|, where I is the identity matrix of order 3 × 3.

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