Mcqs -Matrices and determinants

Matrices and determinants multiple choice questions

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Sub: Mathematics Topic: Matrices and Determinants Type: Practice test
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1. If a matrix has 6 elements, then number of possible orders of the matrix
can be
(a) 2 (b) 4 (c) 3 (d) 6
2. If A = [aij] is a 2 × 3 matrix, such that aij = (−i+2j)^2 / 5.then a23 is

3. If A = diag(3, -1), then matrix A is

4. Total number of possible matrices of order 2 × 3 with each entry 1 or 0 is
(a) 6 (b) 36 (c) 32 (d) 64
5. If A is a square matrix such that A²=A, then (I + A)² – 3A is
(a) I (b) 2A (c) 3I (d) A
6. If matrices A and B are inverse of each other, then
(a) AB = BA (b) AB = BA = I (c) AB = BA = 0 (d) AB = 0, BA = I
7.

8. The diagonal elements of a skew symmetric matrix are
(a) all zeroes (b) are all equal to some scalar k(≠ 0)
(c) can be any number (d) none of these
9. If A = and A = A’ then
(a) x = 0, y = 5 (b) x = y (c) x + y = 5 (d) x – y = 5
10. If a matrix A is both symmetric and skew symmetric then matrix A is
(a) a scalar matrix (b) a diagonal matrix
(c) a zero matrix of order n × n (d) a rectangular matrix.
11.

PRAGNA ACADEMY
30

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12.

13.

14. Solve the following system of equations x – y + z = 4, x – 2y + 2z = 9 and
2x + y + 3z = 1.
(a) x = -4, y = -3, z = 2 (b) x = -1, y = -3, z = 2
(c) x = 2, y = 4, z = 6 (d) x = 3, y = 6, z = 9
15. Find the minor of 6 and cofactor of 4 respectively in the determinant

(a) 6, 6 (b) 6, -6 (c) -6, -6 (d) -6, 6
16. The rank of a non-singular matrix of orer-4
(a)1 (b)2 (c)3 (d)4
17. Consider the following statements and select correct answer.
i) The determinant of a square matrix is zero in case of any one entire row or
column of a matrix is zero
ii) The determinant of a square matrix is zero in case of any two rows or columns
of a matrix is equal or same
iii) The determinant of a rectangular matrix is zero in case of any one entire row
or column of a matrix is zero
iv) The determinant of a rectangular null matrix is zero.
a) Only i is correct b) Only I, ii is correct
c) Only 4 is correct d)All of the above statements are correct.
18. Which of the following statement is false
a) Every Symmetric and skew symmetric matrix are square matrices
b) Every Diagonal matrix is a symmetric matrix
c) Every square matrix is rectangular matrix
d) Every rectangular matrix must be square matrix

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19. Which of the following is not the matrix operation
a) Transpose b) Multiplication c) Scaling d) Reverse
20. If A is a matrix of order 2021 x 2020, then each row of a matrix A consist of
__ Elements and each column of matrix A consist of __ Elements.
a) 2021,2020 b)2020, 2021 c)2020,2020 d)2021,2021
21. If A is an Identity matrix then which of the following is true
a) Matrix A is a square matrix
b) Matrix A is a scalar matrix
c) Matrix A is a non-singular matrix
d) All of the above are true
22. If matrix O represent a null matrix of order n x n then which of the following is
not true
a) Matrix O is a singular matrix as well as square matrix
b) The rank of a Matrix O is 0 for all ‘n’ values
c) The matrix O is non-singular matrix
d)all of the above
23) which of the following is true about inverse of a matrix
a) Inverse of a matrix is only applicable for symmetric matrices
b) The order of matrix is equal to order of its inverse
c) The order of one matrix is equal to reverse of its inverse
d) It is possible to find inverse if matrix is singular
24) Which of the following is not true
a) While transposing a matrix the order will reverse
b) It is possible to multiply two square matrices of same order
c)It is possible to equate two different orders of square matrices
d)Only square matrices have the determinant value
25) Which of the following is true about minor and co factor of an element
a) The minor and co factor of an element aij where i=j is same
b) The minor and co factor of an element aij where i>j is same

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c) The minor and co factor of an element aij where i<j is same
d) All of the above are correct
26) The inverse of a rectangular matrix is 0.
a) True b) false
27) Match the Following table based on
the given matrix

a) 1-F, 2-D,3- C,4-A b) 1-A, 2-D,3- B,4-F
c) 1-F, 2-C,3- A,4-D d)1-F, 2-A,3- D,4-C
28) The det of an orthogonal matrix
a) 0 b)1 c) -1 d) either 1 or -1
29)The system of equations x+y+z=0,2x-y-3z=0, 3x-5y+4z=0 has
a) Unique solution b) No solution c) Infinity Many Solution d) None
30)The number of elements present in a matrix of order 5 x3 is
a) 5 b) 3 c) 15 d) 8

Answer Sheet.
Ques 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
Answer
Ques 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.
Answer

Group-A Group-B
1.The Minor of 9 A. 15
2. The element a14 B. -6
3.The Co-factor of 6 C. 6
4. The Trace of delta matrix D. Can’t find
F. -3
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ANSWERS:
1)B
2)D
3)C
4)D
5)A
6)B
7)D
8)A
9)B
10)C
11) 7 , -1
12)B
13)A
14)B
15)D
16)D
17)B
18)D
19)D
20)B
21)D
22)C
23)B
24)C
25)A
26)B
27)A
28)D
29)A
30)C