Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 11

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If $D_{1}$ and $D_{2}$ are two $3 \times 3$ diagonal matrices, then which of the following is/are true?

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Important Questions on Matrices

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 12

Let

A

be the

2 \times 2

matrix given by

A = [a_{i j}]

where

a_{i j} \in \{0, 1, 2, 3, 4\}

such that

a_{11} + a_{12} + a_{21} + a_{22} = 4

then which of the following statement(s) is/are true?

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 13

If

S = [\begin{matrix} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{matrix}]

and

A = [\begin{matrix} b + c & c - a & b - a \\ c - b & c + b & a - b \\ b - c & a - c & a + b \end{matrix}] (a, b, c \neq 0)

, then

S A S^{- 1}

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 14

P

is non-singular matrix and

A and B

are two matrices such that

B = P^{- 1} A P

. The true statements among the following are

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 15

Let

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

. Then

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 16

If

A = [\begin{matrix} 1 & 0 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0 \end{matrix}]

, then

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 17

If

A

is symmetric and

B

is skew-symmetric matrix, then which of the following is/are CORRECT?

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 18

If

A = {(a_{i j})}_{n \times n}

and

f

is a function, we define

f (A) = {(f (a_{i j}))}_{n \times n}

. Let

A = (\begin{matrix} \frac{π}{2} - θ & θ \\ - θ & \frac{π}{2} - θ \end{matrix})

. Then

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 19

If

A

is a matrix such that

A^{2} + A + 2 I = O

, then which of the following is/are true?