Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 17

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If A is a invertible idempotent matrix of order n, then adj A is equal to

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Important Questions on Matrices and Determinants

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 18

Matrix

A = [\begin{matrix} x & 3 & 2 \\ 1 & y & 4 \\ 2 & 2 & z \end{matrix}]

.

If

x y z = 60

and

8 x + 4 y + 3 z = 20

, then

A (adj A)

is equal to

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 19

Let

A, B, C, D

be (not necessarily square) real matrices such that

A^{T} = B C D; B^{T} = C D A; C^{T} = D A B

and

D^{T} = A B C

for the matrix

S = A B C D

, then which of the following is/are true

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 20

If

A = [\begin{matrix} 1 & \tan x \\ - \tan x & 1 \end{matrix}]

then let us define a function

f (x) = det (A^{T} A^{- 1})

then which of the following can be the value,of

\underset{n t i m e s}{\underset{⏟}{f (f (f (f \dots \dots \dots . . f (x))))}} (n \geq 2)

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 21

If

A

and

B

are two invertible matrices of the same order, then

adj (A B)

is equal to -

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 23

If

A

and

B

are different matrices satisfying

A^{3} = B^{3}

and

A^{2} B = B^{2} A

, then which of the following is/are incorrect :

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 24

If

A = [\begin{array}{l} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array}]

, then-

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 25

Let

Δ_{0} = |\begin{array}{l} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{array}|

(where

Δ_{0} \neq 0

) and let

Δ_{1}

denote the determinant formed by the cofactors of elements of

Δ_{0}

and

Δ_{2}

denote the determinant formed by the cofactors at

Δ_{n - 1}

then the determinant value of

Δ_{n}

is-

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 26

A square matrix can always be expressed as a