Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 13

HARD

JEE Main

IMPORTANT

Earn 100

Number of $3 \times 3$ non-symmetric matrix $A$ such that $A^{T} = A^{2} - I$ and $| A | \neq 0,$ equals to

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Important Questions on Matrices and Determinants

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 14

If A is an orthogonal matrix &

| A | = - 1

, then

A^{T}

is equal to-

HARD

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 16

Which of the following is not true?

MEDIUM

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 17

Let

A = [\begin{array}{l} x & y & z \\ y & z & x \\ z & x & y \end{array}],

where

x, y

and

z

are real numbers such that

x + y + z > 0

and

x y z = 2

. If

A^{2} = I_{3}

, then the value of

x^{3} + y^{3} + z^{3}

is

MEDIUM

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 18

Let

A

be a symmetric matrix of order

2

with integer entries. If the sum of the diagonal elements of

A^{2}

is

1,

then the possible number of such matrices is:

MEDIUM

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 20

If

[\begin{array}{l} 0 2 β γ \\ α β - γ \\ α - β γ \end{array}]

is orthogonal, then the values of

α, β

and

γ

will be

MEDIUM

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 21

Let

A

be a periodic matrix with period

5

and

A^{25} + A^{10} B = I

, then

| A B |

equals to

MEDIUM

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 2>Q 14

A square matrix

A = [\begin{matrix} \cos θ & - \sin θ \\ \sin θ & \cos θ \end{matrix}],

then which of the following statement is not correct?

EASY

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 2>Q 16

If a square matrix

A

is such that

(A^{T} - \frac{1}{2} I) (A - \frac{1}{2} I) = (A^{T} + \frac{1}{2} I) (A + \frac{1}{2} I) = I,

where

I

is a unit matrix, then

A

is