Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 58

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If $A = [\begin{matrix} 0 & 0 & - 1 \\ 0 & - 1 & 0 \\ - 1 & 0 & 0 \end{matrix}]$ then $tr (adj A^{50}) + tr (A^{51}) + 3 tr (A^{- 1}) + 5 (tr ({(A^{2})}^{- 1}))$ is equal to

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Important Questions on Determinants

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 59

A

and

B

are two non-singular matrices such that

A^{6} = I

and

A B^{2} = B A (B \neq I)

, then find the value of

K

so that

B^{K} = I

is

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 60

If

A

is an idempotent matrix satisfying

{(I - \frac{2}{5} A)}^{- 1} = I - α A

, then

α

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 1

If

Δ (n) = |\begin{matrix} x^{n} & \sin x & \cos x \\ n! & \sin \frac{n π}{2} & \cos \frac{n π}{2} \\ α & α^{2} & α^{3} \end{matrix}|

, then the value of

x = 0

is,

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 2

If

s = a + b + c

then the value of

|\begin{matrix} s + c & a & b \\ c & s + a & b \\ c & a & s + b \end{matrix}| =

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 3

The number of distinct real roots of

|\begin{matrix} \sin x & \cos x & \cos x \\ \cos x & \sin x & \cos x \\ \cos x & \cos x & \sin x \end{matrix}| = 0

in the interval

- \frac{π}{4} \leq x \leq \frac{π}{4},

is

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 4

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

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 5

The determinant

D = |\begin{matrix} \cos (α + β) & - \sin (α + β) & \cos 2 β \\ \sin α & \cos α & \sin β \\ - \cos α & \sin α & \cos β \end{matrix}|

is independent of

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 6

If

a, b, c

are sides of the

∆ A B C, |\begin{array}{l} 1 & a & b \\ 1 & c & a \\ 1 & b & c \end{array}| = 0

, then value of

\sin^{2} A + \sin^{2} B + \sin^{2} C

is equal to