Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-2>Q 5

EASY

JEE Main/Advance

IMPORTANT

Earn 100

Find the number of all possible ordered sets of two $(n \times n)$ matrices $A$ and $B$ for which $A B - B A = I$

19.05% studentsanswered this correctly

Important Questions on Matrices and Determinants

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-2>Q 6

If

B, C

are square matrices of order

n

and if

A = B + C, B C = C B, C^{2} = O,

then which of following is true for any positive integer

N .

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-2>Q 7

How many

3 \times 3

skew-symmetric matrices can be formed using numbers

- 2, - 1, 1, 2, 3, 4, 0

(any number can be used any number of times but

0

can be used at most

3

times)

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-2>Q 8

If

A

is a skew-symmetric matrix and

n

is an even positive integer, then

A^{n}

is

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-2>Q 9

Number of

3 \times 3

non-symmetric matrix

A

such that

A^{T} = A^{2} - I

and

| A | \neq 0,

equals to

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-2>Q 10

Matrix

A

is such that

A^{2} = 2 A - I,

where

I

is the identity matrix. Then for

n \geq 2, A^{n} =

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-2>Q 11

If

P = [\begin{matrix} \frac{\sqrt{3}}{2} & \frac{1}{2} \\ - \frac{1}{2} & \frac{\sqrt{3}}{2} \end{matrix}], A = [\begin{array}{l} 1 & 1 \\ 0 & 1 \end{array}]

and

Q = P A P^{T}

and

X = P^{T} Q^{2005} P,

then

X

is equal to

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-2>Q 12

Let

Δ = |\begin{matrix} \sin θ \cos ϕ & \sin θ \sin ϕ & \cos θ \\ \cos θ \cos ϕ & \cos θ \sin ϕ & - \sin θ \\ - \sin θ \sin ϕ & \sin θ \cos ϕ & 0 \end{matrix}|,

then

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-2>Q 13

Δ = |\begin{matrix} 1 + a^{2} + a^{4} & 1 + a b + a^{2} b^{2} & 1 + a c + a^{2} c^{2} \\ 1 + a b + a^{2} b^{2} & 1 + b^{2} + b^{4} & 1 + b c + b^{2} c^{2} \\ 1 + a c + a^{2} c^{2} & 1 + b c + b^{2} c^{2} & 1 + c^{2} + c^{4} \end{matrix}|

is equal to