Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 3

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Let $A$ be an involutory matrix and $S$ be the set containing solution of $A^{x} = I$ . Then minimum value of $\sum_{x \in S}^{\infty} (\sin^{x} θ + \cos^{x} θ)$ (Given that $x \in N$ ).

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Important Questions on Matrices

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Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 5

An orthogonal matrix is

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Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 6

matrix

[\begin{matrix} 0 & - 4 & 1 \\ 4 & 0 & - 5 \\ - 1 & 5 & 0 \end{matrix}]

is

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Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 7

Let

A = [\begin{matrix} 1 & \frac{x}{n} \\ - \frac{x}{n} & 1 \end{matrix}],

then

\lim_{n \to \infty}

A^{n}

is

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Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 8

If

B

is an idempotent matrix and

A = I - B,

then

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Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 9

The matrix

A = [\begin{matrix} i & 1 - 2 i \\ - 1 - 2 i & 0 \end{matrix}]

is which of the following?

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Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 10

If the matrices

A, B

and

A + B

are invertible then

{[A {(A + B)}^{- 1} B]}^{- 1}

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 11

If

[\begin{matrix} x \\ y \\ z \end{matrix}] = \frac{1}{40} [\begin{matrix} 5 & 10 & - 5 \\ - 5 & - 2 & 13 \\ 10 & - 4 & 6 \end{matrix}] [\begin{matrix} 5 \\ 0 \\ 5 \end{matrix}],

then

x + y + z

is

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Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 12

If

A

is a skew symmetric matrix of order

n \times n

and

C

is a column matrix of order

n \times 1

, then

C^{T} A C

is a