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

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If $B$ is an idempotent matrix and $A = I - B,$ then

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Important Questions on Matrices

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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

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Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 13

If

A = [\begin{matrix} α & 3 \\ 2 & 2 α \end{matrix}]

and trace

(A^{2}) = 17,

then the sum of values of

α

is

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Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 15

Let

A = [\begin{matrix} 1 & - 1 & 1 \\ 2 & 1 & - 3 \\ 1 & 1 & 1 \end{matrix}]

and

10 B = [\begin{matrix} 4 & 2 & 2 \\ - 5 & 0 & α \\ 1 & - 2 & 3 \end{matrix}]

. If

B

is the inverse of matrix

A

, then

α

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 16

Let

A = [\begin{matrix} 1 & 3 \\ 3 & 4 \end{matrix}]

and

B = [\begin{matrix} a & 0 \\ 0 & b \end{matrix}], a, b \in N,

then

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Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 1

Let

A (θ) = [\begin{matrix} \cos^{2} θ & \cos θ \sin θ \\ \cos θ \sin θ & \sin^{2} θ \end{matrix}]

and

C (θ, ϕ) = A (θ) A (ϕ),

then which of the following matrices is a null matrix?