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This mock test of Matrix MCQ - 2 for Mathematics helps you for every Mathematics entrance exam.
This contains 30 Multiple Choice Questions for Mathematics Matrix MCQ - 2 (mcq) to study with solutions a complete question bank.
The solved questions answers in this Matrix MCQ - 2 quiz give you a good mix of easy questions and tough questions. Mathematics
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QUESTION: 1

For which value of x will the matrix become singular.

Solution:

QUESTION: 2

A matrix is

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QUESTION: 3

is a 3 X 3 matrix over the set of

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QUESTION: 4

If A = , then A^{2} is

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QUESTION: 5

1 x n matrices are called

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QUESTION: 6

Let f(x) = x^{2 }— 5x + 6 and A = then f (A) is equal

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QUESTION: 7

is called a

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QUESTION: 8

X = [X_{1}, X_{2}, ... , X_{n}] is an n — tuple non — zero vector. Then n x n matrix V = VX

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QUESTION: 9

A submatrix of the given matrix can be obtained by deleting

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QUESTION: 10

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

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QUESTION: 11

Two matrices A and B are said to be comparable if

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QUESTION: 12

Consider the system of equation A_{(nxn)}X_{(nx1)} = λ _{nx1} where, λ is a scalar. Let, (λ_{i}, x_{i}) 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

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QUESTION: 13

If A = and B = then A x B =

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QUESTION: 14

Eigen values of a matrix S = are 5 and 1. What is the eigen values of the matrix S^{2} = SS?

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QUESTION: 15

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

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QUESTION: 16

If 4X = then X

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QUESTION: 17

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

Solution:

Since A is idempotent A^{2} = A

A^{2} - A = 0

m_{A}(x) = x^{2} - x

= x(x-1)

QUESTION: 18

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

Solution:

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?

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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

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QUESTION: 21

If D_{1}, D_{2 }are two diagonal matrices, then

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QUESTION: 22

Matrix multiplication is

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QUESTION: 23

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

Solution:

**R2→R2−R1,R3→R3−R1,R4→R4−R1, and so on**

**Rank of matrix = 1**

QUESTION: 24

Multiplication of matrices E and F is G. Matrices E and G are as follows

Then, the value of matrix F is

Solution:

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 = [x_{1} x_{2} x_{3}]^{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

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QUESTION: 26

Which one of the following is not an elementary operation?

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QUESTION: 27

Which one of the following statements is incorrect for an upper triangular matrix A = (a_{ij})?

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QUESTION: 28

Mark the correct definition of rank of a matrix

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QUESTION: 29

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

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QUESTION: 30

Two matrics Aand B are said to anti — commute if

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