Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-1>Q 46

EASY

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IMPORTANT

Earn 100

Prove that if $A$ is skew symmetric, then $B^{'} A B$ is also skew symmetric.

Important Questions on Matrices and Determinants

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-1>Q 47

[\begin{matrix} x^{2} + x & x \\ 3 & 2 \end{matrix}] + [\begin{matrix} 0 & - 1 \\ - x + 1 & x \end{matrix}] = [\begin{matrix} 0 & - 2 \\ 5 & 1 \end{matrix}]

then

x

is equal to-

EASY

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-1>Q 48

If

A = [\begin{array}{l} 1 \\ 2 \\ 3 \end{array}]

and

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

, then

EASY

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-1>Q 49

If

I = [\begin{array}{l} 1 & 0 \\ 0 & 1 \end{array}], J = [\begin{matrix} 0 & 1 \\ - 1 & 0 \end{matrix}]

and

B = [\begin{matrix} \cos θ & \sin θ \\ - \sin θ & \cos θ \end{matrix}],

then

B =

EASY

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-1>Q 50

In an upper triangular matrix

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

the elements

a_{i j} = 0

for

EASY

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-1>Q 51

If

A = diag (2, - 1, 3), B = diag (- 1, 3, 2),

then

A^{2} B =

MEDIUM

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-1>Q 52

If

A

is a skew- symmetric matrix, then trace of

A

is

EASY

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-1>Q 53

Let

A = [\begin{array}{l} p & q \\ q & p \end{array}]

such that det

(A) = r

where

p, q, r

all prime numbers, then trace of

A

is equal to

HARD

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-1>Q 54

If

A = [\begin{array}{l} 0 & 1 \\ 2 & 0 \end{array}]

and

(A^{8} + A^{6} + A^{4} + A^{2} + I) V = [\begin{array}{l} 31 \\ 62 \end{array}]

, where

I

is the

(2 \times 2)

identity matrix, then the product of all elements of matrix

V

is