Matrix MCQ - 3


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30 Questions MCQ Test Topic-wise Tests & Solved Examples for IIT JAM Mathematics | Matrix MCQ - 3

Matrix MCQ - 3 for Mathematics 2022 is part of Topic-wise Tests & Solved Examples for IIT JAM Mathematics preparation. The Matrix MCQ - 3 questions and answers have been prepared according to the Mathematics exam syllabus.The Matrix MCQ - 3 MCQs are made for Mathematics 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Matrix MCQ - 3 below.
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Matrix MCQ - 3 - Question 1

A matrix A such that A2 = A, is called

Matrix MCQ - 3 - Question 2

Consider the matrix A =  Then,

Matrix MCQ - 3 - Question 3

A matrix A such that A2 = I, is called

Matrix MCQ - 3 - Question 4

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

Matrix MCQ - 3 - Question 5

A square matrix A such the AT = —A, is called a 

Detailed Solution for Matrix MCQ - 3 - Question 5

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

Matrix MCQ - 3 - Question 6

A square matrix A such that AT = -A, is called a

Detailed Solution for Matrix MCQ - 3 - Question 6

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

Matrix MCQ - 3 - Question 7

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

Matrix MCQ - 3 - Question 8

A square matrix A is said to be Hermitian Matrix if 

Detailed Solution for Matrix MCQ - 3 - Question 8

matrix A = [aij] ∈ Mn is said to be Hermitian if A = A or
= aij, for aji only.

Matrix MCQ - 3 - Question 9

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

Detailed Solution for Matrix MCQ - 3 - Question 9

matrix A = [aij] ∈ Mn is skew-Hermitian if A = − A * 

Matrix MCQ - 3 - Question 10

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

Matrix MCQ - 3 - Question 11

Mark the incorrect statement

Matrix MCQ - 3 - Question 12

The diagonal elements of a Skew Hermitian Matrix are

Matrix MCQ - 3 - Question 13

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

Matrix MCQ - 3 - Question 14

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

Matrix MCQ - 3 - Question 15

Every square matrix is uniquely expressible as

Matrix MCQ - 3 - Question 16

If A is any square matrix, then A — A' is a

Detailed Solution for Matrix MCQ - 3 - Question 16

(A − A')' = A' − (A')'

= A' − A

= −(A − A')
Therefore, it is a skew symmetric matrix

Matrix MCQ - 3 - Question 17

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

Matrix MCQ - 3 - Question 18

A square matrix A is said to be ... if AAT = I

Matrix MCQ - 3 - Question 19

If A =  satisfies the matrix equation A2 — kA + 2I = 0, then what is the value of k?

Matrix MCQ - 3 - Question 20

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

Matrix MCQ - 3 - Question 21

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

Matrix MCQ - 3 - Question 22

One of the integrating factor of the differential equation
(y2 – 3xy)dx + (x2 – xy)dy = 0 is 

Detailed Solution for Matrix MCQ - 3 - Question 22

(y2 – 3xy)dx + (x2 – xy) dy = 0;
M = y2 – 3xy, N = x2 – xy
Here differential equation is homogeneous, then
Mx + Ny = xy2 – 3x2y + x2y – xy2 = – 2x2y ≠ 0

Matrix MCQ - 3 - Question 23

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

Matrix MCQ - 3 - Question 24

The product of two Unitary matrices is a ________ matrix

Detailed Solution for Matrix MCQ - 3 - Question 24

the product of two unitary matrices is always unitary.

Matrix MCQ - 3 - Question 25

The points ( x1, y1 ) , ( x2, y2), ( x3, y3) are collinear if the rank of the matrix  is

Matrix MCQ - 3 - Question 26

A neccessary condition for the linear equations a1x + b1 = 0 and a2x + b2 = 0, to have a common solution is that

Matrix MCQ - 3 - Question 27

A necesary and sufficient condition for the linear equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 to possess a unique solution is that

Matrix MCQ - 3 - Question 28

The value of the determinant  is

Matrix MCQ - 3 - Question 29

Which of the following statement is incorrect?

Matrix MCQ - 3 - 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?

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