Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 26

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The greatest value of $x$ satisfying the equation $|\begin{matrix} 2^{11} - x & - 2^{12} & 2^{11} \\ - 2^{12} & 2^{11} - x & 2^{11} \\ 2^{11} & 2^{11} & - 2^{12} - x \end{matrix}| = 0$ is

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Important Questions on Determinants

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 27

The largest value of a third order determinant whose elements are equal to

1

or

0

is

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 28

If

|\begin{matrix} x^{k} & x^{k + 2} & x^{k + 3} \\ y^{k} & y^{k + 2} & y^{k + 3} \\ z^{k} & z^{k + 2} & z^{k + 3} \end{matrix}| = (x - y) (y - z) (z - x) (\frac{1}{x} + \frac{1}{y} + \frac{1}{z})

then

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 29

If all elements of a third order determinant are equal to

1

or

- 1

, then determinant itself is

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 30

If

A

is a

3 \times 3

matrix and

det (3 A) = k {det (A)}

, then

k

is

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 31

If

A

is any of square matrix of order

n

, then

A (adj A)

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 32

If

A

is a square matrix of order

3, | A | = 3

, then

| adj adj A |

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 33

If

A = [\begin{matrix} 11 & 7 \\ - 13 & 17 \end{matrix}]

, then

adj (adj A)

is

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 34

If

A = [\begin{matrix} \sin α & - \cos α & 0 \\ \cos α & \sin α & 0 \\ 0 & 0 & 1 \end{matrix}]

, then

A^{- 1}

is equal to