If 0 2 β γ α β − γ α − β γ is orthogonal, then the values of α , β and γ will be

α = ± 1 2 , β = ± 1 6 , γ = ± 1 3

α = ± 1 5 , β = ± 1 3 , γ = ± 1 2

α = ± 1 6 , β = ± 1 7 , γ = ± 1 3

α = ± 1 3 , β = ± 1 3 , γ = ± 1 3

For k = 1 50 , the value of a , b , c such that P P ′ = I , where P = 2 / 3 3 k a - 1 / 3 - 4 k b 2 / 3 - 5 k c is-

± 13 5 2 , ± 16 5 2 , ∓ 1 3 2

± 16 5 2 , ± 13 5 2 , ∓ 1 3 2

∓ 1 3 2 , ± 13 5 2 , ± 16 5 2

EASY

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The matrix $A = [\begin{matrix} i & 1 - 2 i \\ - 1 - 2 i & 0 \end{matrix}]$ is which of the following ?

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Important Questions on Matrices and Determinants

EASY

Mathematics>Algebra>Matrices and Determinants>Special Types of Matrices

The least positive integer

n

such that

{(\begin{matrix} \cos \frac{π}{4} & \sin \frac{π}{4} \\ - \sin \frac{π}{4} & \cos \frac{π}{4} \end{matrix})}^{n}

is an identity matrix of order

2

EASY

Mathematics>Algebra>Matrices and Determinants>Special Types of Matrices

What is the possible number of different orders, which a matrix can have when it has

24

entries?

EASY

Mathematics>Algebra>Matrices and Determinants>Special Types of Matrices

FInd the number of all possible matrices of order

$3 \times 3$ with each entry $0$ or $1$ .

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Special Types of Matrices

Let

A + 2 B = [\begin{matrix} 1 & 2 & 0 \\ 6 & - 3 & 3 \\ - 5 & 3 & 1 \end{matrix}]

and

2 A - B = [\begin{matrix} 2 & - 1 & 5 \\ 2 & - 1 & 6 \\ 0 & 1 & 2 \end{matrix}] .

T r (A)

denotes the sum of all diagonal elements of the matrix

A,

then

Tr (A) - Tr (B)

has value equal to

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Special Types of Matrices

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}

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Special Types of Matrices

A = [\begin{matrix} a^{2} & 15 & 31 \\ 12 & b^{2} & 41 \\ 35 & 61 & c^{2} \end{matrix}]

and

B = [\begin{matrix} 2 a & 3 & 5 \\ 2 & 2 b & 8 \\ 1 & 4 & 2 c - 3 \end{matrix}]

are two matrices such that the sum of the principal diagonal elements of both

A

and

B

are equal, then the product of the principal diagonal elements of

B

EASY

Mathematics>Algebra>Matrices and Determinants>Special Types of Matrices

M = [m_{i j}]

a

4 \times 4

square matrix, where

i = 1, 2, 3, 4

and

j = 1, 2, 3, 4 .

If in the matrix

M, m_{i j} = \sin (i \times j) x

, then the value of the determinant

| M |

x = \frac{π}{3}

is equal to

HARD

Mathematics>Algebra>Matrices and Determinants>Special Types of Matrices

The number of

3 \times 3

matrices

M

with entries from

{0,1, 2}

, such that the sum of the diagonal elements of

M^{T} M

5

, are

HARD

Mathematics>Algebra>Matrices and Determinants>Special Types of Matrices

A

is a

3 \times 3

non-singular matrix such that

A A^{'} = A^{'} A

and

B = A^{- 1} A^{'},

then

B B^{'}

equals, where

X^{'}

denotes the transpose of the matrix

X

HARD

Mathematics>Algebra>Matrices and Determinants>Special Types of Matrices

Which of the following is (are) NOT the square of a

3 \times 3

matrix with real entries?

EASY

Mathematics>Algebra>Matrices and Determinants>Special Types of Matrices

A

is an orthogonal matrix, then

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Special Types of Matrices

[\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

Mathematics>Algebra>Matrices and Determinants>Special Types of Matrices

A = [\begin{array}{l} p & q & r \\ r & p & q \\ q & r & p \end{array}]

and

A A^{T} = I

, then

p^{3} + q^{3} + r^{3} =

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Special Types of Matrices

If the matrix

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

is orthogonal, then

HARD

Mathematics>Algebra>Matrices and Determinants>Special Types of Matrices

If the matrix

[\begin{matrix} 0 & 2 β & γ \\ α & β & - γ \\ α & - β & γ \end{matrix}]

is orthogonal, then appropriate option will be

EASY

Mathematics>Algebra>Matrices and Determinants>Special Types of Matrices

k . [\begin{array}{l} - 1 & 2 & 2 \\ 2 & - 1 & 2 \\ 2 & 2 & - 1 \end{array}]

is an orthogonal matrix, then k is equal to-

EASY

Mathematics>Algebra>Matrices and Determinants>Special Types of Matrices

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

is an orthogonal matrix, then the number of possible triplets

(α, β, γ)

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Special Types of Matrices

A

is an involuntary matrix given by

A = [\begin{array}{l} 0 & 1 & - 1 \\ 4 & - 3 & 4 \\ 3 & - 3 & 4 \end{array}]

then the inverse of

\frac{A}{2}

will be

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Special Types of Matrices

For

k = \frac{1}{\sqrt{50}}

, the value of

a, b, c

such that

P P' = I

, where

P = [\begin{array}{l} 2 / 3 & 3 k & a \\ - 1 / 3 & - 4 k & b \\ 2 / 3 & - 5 k & c \end{array}]

is-

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Special Types of Matrices

i = \sqrt{- 1}, a = \frac{1 + \sqrt{5}}{2}, b = \frac{1 - \sqrt{5}}{2}

, then which of the following matrix is idempotent?

The matrix A = i 1 - 2 i - 1 - 2 i 0 is which of the following ?

Important Questions on Matrices and Determinants

Learn and Prepare for any exam you want !

The matrix $A = [\begin{matrix} i & 1 - 2 i \\ - 1 - 2 i & 0 \end{matrix}]$ is which of the following ?