Matrix MCQ - 1


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20 Questions MCQ Test Topic-wise Tests & Solved Examples for IIT JAM Mathematics | Matrix MCQ - 1

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

If a, b, h are real number, then the roots of the equation  are

Matrix MCQ - 1 - Question 2

Let A  =  be expressed as P + Q, where P is symmetric matrix and Q is Skew — symmetric matrix. Which one of the following is correct?

Matrix MCQ - 1 - Question 3

 can be written as a sum of a determinants

Matrix MCQ - 1 - Question 4

If the system of equations x — 2y — 3z = 1, ( P + 2 )z = 3, (2 P + l ) y + z = 2 inconsistent, then value of P is

Matrix MCQ - 1 - Question 5

Matrix MCQ - 1 - Question 6

The value of  is equal to 

Matrix MCQ - 1 - Question 7

The values of the minors of the elements of the first row of the determinant  are respectively

Matrix MCQ - 1 - Question 8

The system of linear equation 
x – y + 2z = b1 
x + 2y – z = b2 
2y – 2z = b3 
is inconsistent when (b1, b2, b3) equals 

Detailed Solution for Matrix MCQ - 1 - Question 8

The system of linear equation
x – y + 2z = b1
x + 2y – z = b2
2y – 2z = b2 


Apply



System is in consistent if

Matrix MCQ - 1 - Question 9

The system of equations 
2x + 2y – 3z = 1, 
4x + 4y + z = 2, 
6x + 6y – z = 3 has 

Detailed Solution for Matrix MCQ - 1 - Question 9

The matrix form of the system of equation is AX = b

The augmented matrix is

Applying R2 → R2 - 2R1 , R3  → R3 - 3R1, we have



Apply R3 → R3 - 8R2

Hence, the rank of the matrix is equal to 2 i.e. r ( A | b) = 2.
Here, rank(A) = 2 = rank[A|b] < no of unknowns = 3. So there are infinite many solution of the system of equations.

Matrix MCQ - 1 - Question 10

Square matrix A of order n over R has rank n. Which one of the following statement is not correct?

Detailed Solution for Matrix MCQ - 1 - Question 10

Since, if A is a square matrix of rank n, then it cannot be a singular

Matrix MCQ - 1 - Question 11

The system of equations

Matrix MCQ - 1 - Question 12

The given system of equation

*Multiple options can be correct
Matrix MCQ - 1 - Question 13

The matrix addition is

*Multiple options can be correct
Matrix MCQ - 1 - Question 14

Which of the following statements is/are correct. The trace of a matrix A =  is defined by Tr(A) = a11 + a22 

Matrix MCQ - 1 - Question 15

Which of the following statements is correct? 

Detailed Solution for Matrix MCQ - 1 - Question 15

Correct Answer :- a

Explanation : Properties of Transpose :

(A + B)T = AT + BT 

(kA)T = kAT

*Multiple options can be correct
Matrix MCQ - 1 - Question 16

Which of the following(s) is/are correct?

*Multiple options can be correct
Matrix MCQ - 1 - Question 17

Which of the following(s) is/are correct?

*Multiple options can be correct
Matrix MCQ - 1 - Question 18

Which of the following(s) is/are correct?

*Multiple options can be correct
Matrix MCQ - 1 - Question 19

Which of the following(s) is/are correct?

*Multiple options can be correct
Matrix MCQ - 1 - Question 20

Which of the following(s) is/are correct?

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