Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-1>Q 45

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Let $A^{- 1} = B C$ then the value of $tr (A B C + B C A + C A B)$ is equal to (where the order of matrices $A$ , $B$ , $C$ is $3$ & $t r (A)$ is sum of diagonal elements $A$ )

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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-1>Q 46

If

A

is a non singular square matrix where

B = A^{T}

&

A + B^{2} = I

, such that

A^{3} + I = k A

then

k

is equal to

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 1

Which of the following determinant(s) vanish(es)?

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

If

f^{'} (x) = |\begin{matrix} m x & m x - p & m x + p \\ n & n + p & n - p \\ m x + 2 n & m x + 2 n + p & m x + 2 n - p \end{matrix}|

, then

y = f (x)

represents

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 3

The determinant

|\begin{matrix} a^{2} & a^{2} - (b - c)^{2} & b c \\ b^{2} & b^{2} - (c - a)^{2} & c a \\ c^{2} & c^{2} - (a - b)^{2} & a b \end{matrix}|

is divisible by -

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 4

The determinant

|\begin{matrix} a & b & a α + b \\ b & c & b α + c \\ a α + b & b α + c & 0 \end{matrix}|

is equal to zero, if -

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 6

The parameter on which the value of the determinant

|\begin{matrix} 1 & a & a^{2} \\ \cos (p - d) x & \cos p x & \cos (p + d) x \\ \sin (p - d) x & \sin p x & \sin (p + d) x \end{matrix}|

does not depend upon, is

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 7

If

a^{2} + b^{2} + c^{2} = - 2

and

f (x) = |\begin{matrix} 1 + a^{2} x & (1 + b^{2}) x & (1 + c^{2}) x \\ (1 + a^{2}) x & 1 + b^{2} x & (1 + c^{2}) x \\ (1 + a^{2}) x & (1 + b^{2}) x & 1 + c^{2} x \end{matrix}|

, then

f (x)

is a polynomial of degree

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 8

Given that

q^{2} - p r < 0, p, q, r > 0

, then the value of

|\begin{matrix} p & q & p x + q y \\ q & r & q x + r y \\ p x + q y & q x + r y & 0 \end{matrix}|

is-