Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 34

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The multiplicative inverse of matrix $A = [\begin{array}{l} 2 & 1 \\ 7 & 4 \end{array}]$ is

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Important Questions on Matrices

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Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 35

The matrix

X

in the equation

A X = B

, such that

A = [\begin{matrix} 1 & 3 \\ 0 & 1 \end{matrix}]

and

B = [\begin{matrix} 1 & - 1 \\ 0 & 1 \end{matrix}]

is given by

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Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 37

Let

A = {[a_{i j}]}_{50 \times 50}

such that

a_{i j} = \tan^{- 1} (i - j), \forall i, j

, then

\sum a_{i j}

, is

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Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 38

Let a set

A = \{a_{1}, a_{2}, a_{3}, \dots, a_{180}\}

. Then total number of possible matrices of different order formed by using all element of set

A

exactly once in a matrix is

n_{1} \cdot (n_{2}!)

, where

n_{1}, n_{2} \in N

. Then least value of

(n_{1} + n_{2})

is

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Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 39

A

and

B

are two

3 \times 3

matrices such that they are inverse of each other then

t r . (5 A B + 6 B A + 7 {(A B)}^{2} + 8 {(B A)}^{2})

is equal to

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

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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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