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This mock test of Matrix MCQ - 3 for Mathematics helps you for every Mathematics entrance exam.
This contains 30 Multiple Choice Questions for Mathematics Matrix MCQ - 3 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

A matrix A such that A^{2 }= A, is called

Solution:

QUESTION: 2

Consider the matrix A = Then,

Solution:

QUESTION: 3

A matrix A such that A^{2} = I, is called

Solution:

QUESTION: 4

A matrix A such that A^{m} = 0 for some positive integer and A^{k} ≠ 0 for any k < m, is said to be

Solution:

QUESTION: 5

A square matrix A such the A^{T }= —A, is called a

Solution:

Transpose of a matrix happens to be equal to the negative of itself, then one can say that the matrix is skew symmetric.

QUESTION: 6

A square matrix A such that A^{T} = -A, is called a

Solution:

In mathematics, particularly in linear algebra, a skew-symmetric matrix is a square matrix whose transpose equals its negative.

QUESTION: 7

Mark the in correct statement. If A* and B* are the transpose of the conjugates of A and B respectively, the n

Solution:

QUESTION: 8

A square matrix A is said to be Hermitian Matrix if

Solution:

A **matrix** A = [a_{ij}] ∈ M_{n} is **said to be Hermitian if** A = A^{* } or

= a_{ij}, for a_{ji} only.

QUESTION: 9

A square matrix A is said to be Skew Hermitian Matrix, if

Solution:

A **matrix** A = [a_{ij}] ∈ M_{n} is skew-**Hermitian if** A = − A ^{*}

QUESTION: 10

If A and B are two odd order Skew — symmetric matrices such that AB = BA, then what is the matrix AB?

Solution:

QUESTION: 11

Mark the incorrect statement

Solution:

QUESTION: 12

The diagonal elements of a Skew Hermitian Matrix are

Solution:

QUESTION: 13

To convert a Hermitian Matrix into Skew Hermitian Matrix, the Hermitian Matrix must be multiplied by

Solution:

QUESTION: 14

Which is not correct? If A is any square matrix, then... is Hermitian Matrix

Solution:

QUESTION: 15

Every square matrix is uniquely expressible as

Solution:

QUESTION: 16

If A is any square matrix, then A — A^{'} is a

Solution:

(A − A')' = A' − (A')'

= A' − A

= −(A − A')

Therefore, it is a skew symmetric matrix

QUESTION: 17

If A and B are symmetric matrices of the same order, then which one of the following is not correct?

Solution:

QUESTION: 18

A square matrix A is said to be ... if AA^{T} = I

Solution:

QUESTION: 19

If A = satisfies the matrix equation A^{2} — kA + 21 = 0, then what is the value of k?

Solution:

QUESTION: 20

A square matirx A is said to be .... if A* A = I

Solution:

QUESTION: 21

Under which one of the following condition does the system of equations have a unique solution?

Solution:

QUESTION: 22

One of the integrating factor of the differential equation

(y^{2} – 3xy)dx + (x^{2 }– xy)dy = 0 is

Solution:

(y^{2} – 3xy)dx + (x^{2} – xy) dy = 0;

M = y^{2} – 3xy, N = x^{2} – xy

Here differential equation is homogeneous, then

Mx + Ny = xy^{2} – 3x^{2}y + x^{2}y – xy^{2} = – 2x^{2}y ≠ 0

QUESTION: 23

The product of two orthogonal matrices is a ... matrix

Solution:

QUESTION: 24

The product of two Unitary matrices is a ________ matrix

Solution:

the product of two unitary matrices is always unitary.

QUESTION: 25

The points ( x_{1, }y_{1} ) , ( x_{2}, y_{2}), ( x_{3,} y_{3}) are collinear if the rank of the matrix is

Solution:

QUESTION: 26

A neccessary condition for the linear equations a_{1}x + b_{1} = 0 and a_{2}x + b_{2} = 0, to have a common solution is that

Solution:

QUESTION: 27

A necesary and sufficient condition for the linear equations a_{1}x + b_{1}y + c_{1} = 0 and a_{2}x + b_{2}y + c_{2} = 0 to possess a unique solution is that

Solution:

QUESTION: 28

The value of the determinant is

Solution:

QUESTION: 29

Which of the following statement is incorrect?

Solution:

QUESTION: 30

Let A and B be any two n x n matrices and tr(A) = Consider the following statement

I. tr(AB) = tr(BA)

II. tr(A + B) = tr. (A) + tr(B)

Which of the following statement given above is/are correct?

Solution:

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