Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 13 - Matrices>Practice Exercise>Q 18

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IMPORTANT

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If $A$ is any matrix, then the product $A A$ is defined only when $A$ is a matrix of order $m \times n$ , where

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Important Questions on Matrices

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IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 13 - Matrices>Practice Exercise>Q 19

If

A = [\begin{matrix} 4 & x + 2 \\ 2 x - 3 & x + 1 \end{matrix}]

is symmetric, then what is

x

equal to

?

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IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 13 - Matrices>Practice Exercise>Q 20

If $A$ and $B$ be two matrices such that $A B = A$ and $B A = B$ . Then, which of the following statement(s) is $/$ are correct $?$

$I$ . $A^{2} = A$

$II$ , $B^{2} = B$

$III$ . ${(A B)}^{2} = A B$

Select the correct answer using the code given below.

EASY

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IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 13 - Matrices>Practice Exercise>Q 21

Which one of the following matrices is an elementary matrix

?

EASY

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IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 13 - Matrices>Practice Exercise>Q 22

The matrix

[\begin{matrix} 0 & - 4 + i \\ 4 + i & 0 \end{matrix}]

is

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IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 13 - Matrices>Practice Exercise>Q 23

If

X = [\begin{array}{l} 3 & - 4 \\ 1 & - 1 \end{array}], B = [\begin{matrix} 5 & 2 \\ - 2 & 1 \end{matrix}]

and

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

satisfy the equation

A X = B

, then the matrix

A

is equal to

EASY

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IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 13 - Matrices>Practice Exercise>Q 24

Let

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

and

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

. If

A B = C

, then what is

A^{2}

equal to

?

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 13 - Matrices>Practice Exercise>Q 25

If

E (θ) = [\begin{matrix} \cos θ & \sin θ \\ - \sin θ & \cos θ \end{matrix}]

, then

E (α) E (β)

is equal to

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 13 - Matrices>Practice Exercise>Q 26

If

A = [\begin{array}{r} 1 & 0 & - 2 \\ 2 & - 3 & 4 \end{array}]

, then the matrix

X

for which

2 X + 3 A = 0

holds true is