Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 40

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If $A$ and $B$ are orthogonal matrices of order $4 \times 4$ and $5 \times 5$ respectively then $t r . (A A^{T} + 2 A^{T} A + 5 (A A^{T}) + t r . (2 B B^{T} + 4 B^{T} B))$ is

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Important Questions on Matrices

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Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 41

Let

A = [\begin{matrix} 3 & 1 \\ - 16 & - 5 \end{matrix}]

, then the sum of all the elements of

A^{50}

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 43

If

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

and

A^{T} A = A A^{T} = I,

then

x y

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 44

Let

A = [\begin{matrix} - 5 & - 8 & 0 \\ 3 & 5 & 0 \\ 1 & 2 & - 1 \end{matrix}]

and

B = A + A^{2} + A^{4} + A^{8} + . . . . + A^{2^{78}}

then sum of all the elements of matrix

B

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 2

Let $t$ be the trace of the matrix

$A = [\begin{matrix} \frac{|x + y|}{|x| + |y|} & α_{1} & β_{1} \\ α_{2} & \frac{|y + z|}{|y| + |z|} & β_{2} \\ α_{3} & β_{3} & \frac{|z + x|}{|z| + |x|} \end{matrix}],$ then

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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 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