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

EASY

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IMPORTANT

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

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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 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

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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

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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

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 13 - Matrices>Practice Exercise>Q 27

If $A = [\begin{matrix} 1 & 1 & - 1 \\ 2 & - 3 & 4 \\ 3 & - 2 & 3 \end{matrix}]$ and $B = [\begin{matrix} - 1 & - 2 & - 1 \\ 6 & 12 & 6 \\ 5 & 10 & 5 \end{matrix}]$ , then Which of the following is/are correct $?$

$I$ . $A$ and $B$ commute

$II$ . $A B$ is a null matrix. Select the correct answer using the code given below.

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 13 - Matrices>Practice Exercise>Q 28

Consider the following in respect of the matrix

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

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

$II$ . $A^{3} = 4 A$

Which of the above statement(s) is/are correct?