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

HARD

JEE Main/Advance

IMPORTANT

Earn 100

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

50% studentsanswered this correctly

Important Questions on Matrices

HARD

JEE Main/Advance

IMPORTANT

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?

EASY

JEE Main/Advance

IMPORTANT

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?

MEDIUM

JEE Main/Advance

IMPORTANT

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?

MEDIUM

JEE Main/Advance

IMPORTANT

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

MEDIUM

JEE Main/Advance

IMPORTANT

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

HARD

JEE Main/Advance

IMPORTANT

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

MEDIUM

JEE Main/Advance

IMPORTANT

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

HARD

JEE Main/Advance

IMPORTANT

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?