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Matrix MCQ - 2 - Mathematics MCQ


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30 Questions MCQ Test - Matrix MCQ - 2

Matrix MCQ - 2 for Mathematics 2024 is part of Mathematics preparation. The Matrix MCQ - 2 questions and answers have been prepared according to the Mathematics exam syllabus.The Matrix MCQ - 2 MCQs are made for Mathematics 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Matrix MCQ - 2 below.
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Matrix MCQ - 2 - Question 1

For which value of x will the matrix   become singular.

Matrix MCQ - 2 - Question 2

A matrix is

Detailed Solution for Matrix MCQ - 2 - Question 2

Explanation:


  • A matrix is an arrangement of mn numbers: In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. Each number in a matrix is called an element. The number of rows and columns in a matrix determine its dimensions.

  • Over the given set S: The elements of a matrix can be real numbers, complex numbers, integers, or any other type of mathematical objects. The set S specifies the type of elements that can be included in the matrix.

  • In a rectangular array of m rows and n columns: A matrix is usually represented as m x n, where m represents the number of rows and n represents the number of columns. The elements of the matrix are placed in the respective rows and columns to form the rectangular array.

  •  
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Matrix MCQ - 2 - Question 3

 
is a 3 X 3 matrix over the set of

Matrix MCQ - 2 - Question 4

If A = ,  then A2 is

Matrix MCQ - 2 - Question 5

1 x n matrices are called 

Matrix MCQ - 2 - Question 6

Let f(x) = x2 — 5x + 6 and A =  then f (A) is equal

Matrix MCQ - 2 - Question 7

 is called a

Matrix MCQ - 2 - Question 8

X = [X1, X2, ... , Xn] is an n — tuple non — zero vector. Then n x n matrix V = VX 

Matrix MCQ - 2 - Question 9

A submatrix of the given matrix can be obtained by deleting

Matrix MCQ - 2 - Question 10

Consider a non — homogeneous system of linear equation represented mathematically an over determined system. Such a system will be

Matrix MCQ - 2 - Question 11

Two matrices A and B are said to be comparable if

Matrix MCQ - 2 - Question 12

Consider the system of equation A(nxn)X(nx1) = λ nx1 where, λ is a scalar. Let, (λi, xi) be an eigen pair of an eigen value and its corresponding eigen vector for real matrix A. Let I be a (n x n) unit matrix. Which one of the following statements is not correct

Matrix MCQ - 2 - Question 13

If A =  and B =  then A x B =

Matrix MCQ - 2 - Question 14

Eigen values of a matrix S =  are 5 and 1. What is the eigen values of the matrix S2 = SS?

Detailed Solution for Matrix MCQ - 2 - Question 14

For S matrix, if eigen values are λ1, λ2, λ3,... then for S² matrix, the eigen values will be λ²1 λ²2 λ²3 ,, ,....
For S matrix, if eigen values are 1 and 5 then for S² matrix, the eigen values are 1 and 25

Matrix MCQ - 2 - Question 15

If A is non - scalar, non - identity idempotent matrix of order n ≥ 2. Then, minimal polynomial mA(x) is

Matrix MCQ - 2 - Question 16

If 4X =  then X

Matrix MCQ - 2 - Question 17

If A is a non scalar non identity idempotent matrix of order n≥2. the minimal polynomial mA(x) is

Detailed Solution for Matrix MCQ - 2 - Question 17

Since A is idempotent A2 = A

A2 - A = 0

mA(x) = x2 - x

= x(x-1)

Matrix MCQ - 2 - Question 18

If A =  and B =  then AB is a matrix of order

Matrix MCQ - 2 - Question 19

All the four entries of the 2 x 2 matrix P =  are non - zero, and one of its eigen values is zero . Which one of the following statements is true?

Matrix MCQ - 2 - Question 20

In the matrix equation PX = q, which of the following is necessary condition for the existence of atleast one solution for the unknown vector

Matrix MCQ - 2 - Question 21

If D1, Dare two diagonal matrices, then 

Detailed Solution for Matrix MCQ - 2 - Question 21

Matrix MCQ - 2 - Question 22

Matrix multiplication is

Matrix MCQ - 2 - Question 23

The rank of the following (n + 1 ) x (n + 1) matrix where a is the real number 

Detailed Solution for Matrix MCQ - 2 - Question 23

R2→R2−R1,R3→R3−R1,R4→R4−R1, and so on

Rank of matrix = 1

Matrix MCQ - 2 - Question 24

Multiplication of matrices E and F is G. Matrices E and G are as follows
 Then, the value of matrix F is

Matrix MCQ - 2 - Question 25

The linear operator L(x) is defined by the cross product L(x) = b x X, where b = [0 1 0]T and X = [x1 x2 x3]T are three dimensional vectors. The 3 x 3 matrix M o f this operation satisfies L (x ) =  Then, the eigen values of M are

Matrix MCQ - 2 - Question 26

Which one of the following is not an elementary operation?

Matrix MCQ - 2 - Question 27

Which one of the following statements is incorrect for an upper triangular matrix A = (aij)?

Matrix MCQ - 2 - Question 28

Mark the correct definition of rank of a matrix

Matrix MCQ - 2 - Question 29

The rank of matrix  a, b, c, being all real, is 3 if

Matrix MCQ - 2 - Question 30

Two matrics Aand B are said to anti — commute if

Detailed Solution for Matrix MCQ - 2 - Question 30

Explanation:

  • Anti-commuting Property: For two matrices AAA and BBB, they are said to anti-commute if the product ABABAB is equal to the negative of the product BABABA. This means:

    AB=−BA
  • Option Analysis:

    1. AB=BA: This defines matrices that commute, not anti-commute.
    2. AB^2=A^2B: This does not describe anti-commutation; it is a different property involving matrix powers.
    3. AB=−BA: This correctly describes anti-commutation.
    4. A/B=B/A: This is not a standard matrix operation and does not relate to anti-commutation.

Answer: AB=−BA

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