MEDIUM

Earn 100

If $A$ is a non-null diagonal matrix of order $3$ such that $A^{4} = A^{2},$ then the possible number of matrices $A$ are

30.77% studentsanswered this correctly

Important Questions on Matrices and Determinants

EASY

Mathematics>Algebra>Matrices and Determinants>Basics of Matrices

FInd the number of all possible matrices of order

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

EASY

Mathematics>Algebra>Matrices and Determinants>Basics of Matrices

For a

3 \times 4

matrix, elements are given by

a_{i j} = | - 3 i + 4 j |

, then

\sum_{i = 1}^{3} {(a_{i i})}^{i} =___

EASY

Mathematics>Algebra>Matrices and Determinants>Basics of Matrices

If matrix

A

{(a_{i j})}_{m \times n}

and

B

{(b_{j k})}_{n \times p}

then the order of the matrix

AB

EASY

Mathematics>Algebra>Matrices and Determinants>Basics of Matrices

Consider the following statements :
(I) There exists a square matrix with

12

elements
(II) There exists a zero matrix with

12

elements

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Basics 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

EASY

Mathematics>Algebra>Matrices and Determinants>Basics of Matrices

Let

A = [a_{i j}]

be a

2 \times 2

matrix with

a_{i j} = (- 1)^{j} i^{2} .

Then the matrix

A

is given by

EASY

Mathematics>Algebra>Matrices and Determinants>Basics of Matrices

A = {[a_{i j}]}_{n \times n}

such that

a_{i j} = 0

, for

i \neq j

, then

A

is _____

(a_{i i} \neq a_{j j}), (n > 1)

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Basics of Matrices

[\begin{matrix} a_{1} + a_{2} & 4 \\ 3 & a_{3} + a_{4} \end{matrix}] - [\begin{matrix} 3 a_{2} & 3 a_{1} \\ 3 a_{4} & 3 a_{3} \end{matrix}] = [\begin{matrix} - 6 & - a_{1} \\ - 2 a_{4} & 1 \end{matrix}]

, then

\sum_{i = 1}^{4} a_{i} =

EASY

Mathematics>Algebra>Matrices and Determinants>Basics 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>Basics 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>Basics 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

EASY

Mathematics>Algebra>Matrices and Determinants>Basics 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

HARD

Mathematics>Algebra>Matrices and Determinants>Basics of Matrices

Let $a, b, c \in R$ be all non-zero and satisfies $a^{3} + b^{3} + c^{3} = 2$ . If the matrix $A = [\begin{matrix} a & b & c \\ b & c & a \\ c & a & b \end{matrix}] \begin{array}{l} \end{array}$ satisfies $A^{T} A = I,$ then a value of $a b c$ can be

EASY

Mathematics>Algebra>Matrices and Determinants>Basics of Matrices

The matrix

[\begin{matrix} 1 & 0 \\ 2 & - 1 \\ 0 & - 2 \end{matrix}]

has the order

EASY

Mathematics>Algebra>Matrices and Determinants>Basics of Matrices

Which of the given values of $x$ and $y$ make the following pair of matrices equal?

$[\begin{matrix} 3 x + 7 & 5 \\ y + 1 & 2 - 3 x \end{matrix}]$ and $[\begin{matrix} 0 & y - 2 \\ 8 & 4 \end{matrix}]$

EASY

Mathematics>Algebra>Matrices and Determinants>Basics of Matrices

[\begin{array}{cc} 2 x & 3 \\ 0 & 1 \end{array}] = [\begin{array}{cc} 2 & 3 \\ 0 & 1 \end{array}]

then the value of

x

will be

EASY

Mathematics>Algebra>Matrices and Determinants>Basics of Matrices

A = [\begin{array}{cc} a & b \\ c & - a \end{array}]

is such that

A^{2} = I

, then

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Basics 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>Basics of Matrices

The trace of the matrix

A = [\begin{matrix} 1 & - 5 & 7 \\ 0 & 7 & 9 \\ 11 & 8 & 9 \end{matrix}]

MEDIUM

Mathematics>Algebra>Matrices and Determinants>Basics of Matrices

The number of possible matrices of order

3 \times 3

with each entry

0

1

If A is a non-null diagonal matrix of order 3 such that A4=A2, then the possible number of matrices A are

Important Questions on Matrices and Determinants

Learn and Prepare for any exam you want !

If $A$ is a non-null diagonal matrix of order $3$ such that $A^{4} = A^{2},$ then the possible number of matrices $A$ are