Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 7

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If $B$ is an idempotent matrix, and $A = I - B$ , then

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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 8

If

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

and

A_{2} = [\begin{matrix} 0 & 0 & 0 & i \\ 0 & 0 & - i & 0 \\ 0 & i & 0 & 0 \\ - i & 0 & 0 & 0 \end{matrix}]

, then

A_{i} A_{k} + A_{k} A_{i}

is equal to

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 9

Suppose

a_{1}, a_{2}, a_{3}, . . .

are real numbers, with

a_{1} \neq 0 .

If

a_{1}, a_{2}, a_{3} . . . . .

are in

A . P .,

then

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 10

If

α, β and γ

are three real numbers and

A = [\begin{matrix} 1 & \cos (α - β) & \cos (α - γ) \\ \cos (β - α) & 1 & \cos (β - γ) \\ \cos (γ - α) & \cos (γ - β) & 1 \end{matrix}]

then which of following is/are true?

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

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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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