Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 1 - Matrix>Target Exercises>Q 12

MEDIUM

JEE Advanced

IMPORTANT

Earn 100

If $A = [\begin{array}{l} 1 & 1 \\ 1 & 1 \end{array}]$ , then $A^{100}$ is equal to

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Important Questions on Matrix

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 1 - Matrix>Target Exercises>Q 13

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

is equal to

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 1 - Matrix>Target Exercises>Q 14

If

A

and

B

are square matrices of the same order and

A B = 3 I

, then

A^{- 1}

is equal to

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 1 - Matrix>Target Exercises>Q 15

If

A

and

B

are square matrices of the same order such that

(A + B) (A - B) = A^{2} - B^{2}

, then

{(A B A^{- 1})}^{2}

is equal to

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 1 - Matrix>Target Exercises>Q 16

If

A

and

B

are two square matrices such that

A B = A

and

B A = B

, then

A

and

B

are

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 1 - Matrix>Target Exercises>Q 17

For

k = \frac{1}{\sqrt{50}}

, the values of

a, b, c

such that

P P^{'} = I

, where

P = [\begin{matrix} \frac{2}{3} & 3 k & a \\ \frac{- 1}{3} & - 4 k & b \\ \frac{2}{3} & - 5 k & c \end{matrix}]

, are

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 1 - Matrix>Target Exercises>Q 18

If

A^{2} = A

, then

{(I + A)}^{4}

is equal to

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 1 - Matrix>Target Exercises>Q 19

If

A

is a

2 \times 2

matrix such that

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

and

A^{2} [\begin{matrix} 1 \\ - 1 \end{matrix}] = [\begin{array}{l} 1 \\ 0 \end{array}]

. Then, the sum of the elements of

A

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 1 - Matrix>Target Exercises>Q 20

If $A = [\begin{array}{l} a & b \\ 0 & a \end{array}]$ is $n^{th}$ root of $I_{2}$ , then choose the correct statements.

$I .$ If $n$ is odd, then $a = 1, b = 0$

$II .$ If $n$ is odd, then $a = - 1, b = 0$

$III .$ If $n$ is even, then $a = 1, b = 0$

$IV .$ If $n$ is even, then $a = - 1, b = 0$