Engineering Entrance Sample Papers

multiple choice questions on Matrices and Determinants

Matrices and Determinants mcq

MCQ on Matrices and Determinants:

Ques. If the system of equations, x + 2y – 3z = 1, (k + 3)z = 3, (2k + 1)x + z = 0 is inconsistent, then the value of k is
(a) – 3
(b) ½
(c) 0
(d) 2
Ans. (a)

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Ques. For any square matrix A, AAT is a
(a) Unit matrix
(b) Symmetric matrix
(c) Skew symmetric matrix
(d) Diagonal matrix
Ans. (b)

Ques. If the system of equations x + ay = 0, az + y = 0 and ax + z = 0 has infinite solutions, then the value of a is
(a) –1
(b) 1
(c) 0
(d) No real values
Ans. (a)

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Ques. If the system of equations x – ky – z = 0, kx – y – z = 0 and x + y – z = 0 has a non zero solution, then the possible value of k are
(a) – 1, 2
(b) 1, 2
(c) 0, 1
(d) – 1, 1
Ans. (d)

Ques. For two invertible matrices A and B  of suitable orders, the  value of (AB)–1 is
(a) (BA)–1
(b) B–1 A–1
(c) A–1 B–1
(d) (AB’)–1
Ans. (b)

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Ques. The matrix product AB = O, then
(a) A = O and B = O
(b) A = O or B = O
(c) A is null matrix
(d) None of these
Ans. (d)

Ques. The number of solution of the following equations x2 – x3 = 1, –x1 + 2x3 = –2, x1 – 2x2 = 3 is
(a) Zero
(b) One
(c) Two
(d) Infinite
Ans. (a)

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Ques. f I  is a unit matrix, then 3I will be
(a) A unit matrix
(b) A triangular matrix
(c) A scalar matrix
(d) None of these
Ans. (c)

Ques. If the system of linear equation x + 2ay + az = 0, x + 3by + bz = 0, x + 4cy + cz = 0 has a non zero solution, then a, b, c
(a) Are in A.P.
(b) Are in G. P.
(c) Are in H. P.
(d) Satisfy a + 2b + 3c = 0
Ans. (c)

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Ques. Which of the following is not true?
(a) Every skew-symmetric matrix of odd order is non-singular
(b) If determinant of a square matrix is non-zero, then it is non singular
(c) Adjoint of symmetric matrix is symmetric
(d) Adjoint of a diagonal matrix is diagonal
Ans. (a)

Ques. The values of x, y, z in order of the system of equations 3x + y + 2z = 3, 2x – 3y – z = –3, x + 2y + z = 4, are
(a) 2, 1, 5
(b) 1, 1, 1
(c) 1, –2, –1
(d) 1, 2, –1
Ans. (d)

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Ques. If a matrix A is such that 3A3 + 2A2 + 5A + I = 0 then its inverse is
(a) –(3A2 + 2A + 5I)
(b) 3A2 + 2A + 5I
(c) 3A2 – 2A – 5I
(d) None of these
Ans. (a)

Ques. Choose the correct answer
(a) Every identity matrix is a scalar matrix
(b) Every scalar matrix is an identity matrix
(c) Every diagonal matrix is an identity matrix
(d) A square matrix whose each element is 1 is an identity matrix
Ans. (a)

Ques. Which is true about matrix multiplication?
(a) It is commutative
(b) It is associative
(c) Both (a) and (b)
(d) None of these
Ans. (b)

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Ques. The system of equations x1 – x2 + x3 = 2, 3x1 – x2 + 2x3 = –6 and  3x1 + x2 + x3 = –18 has
(a) No solution
(b) Exactly one solution
(c) Infinite solutions
(d) None of these
Ans. (c)

Ques. If A2 – A + I = 0, then A–1 =
(a) A–2
(b) A + I
(c) I – A
(d) A – I
Ans. (c)

Ques. If A and B are square matrices of order 2, then (A + B)2 =
(a) A2 + 2AB + B2
(b) A2 + AB + BA + B2
(c) A2 + 2BA + B2
(d) None of these
Ans. (b)

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Ques. The number of values of k for which the system of equations (k + 1)x + 8y = 4k, kx + (k + 3)y = 3k – 1 has infinitely many solutions, is
(a) 0
(b) 1
(c) 2
(d) Infinite
Ans. (b)

Ques. If A and B are square matrices of order 3 such that | A | = –1, | B | = 3,  then | 3AB | =
(a) – 9
(b) – 81
(c) – 27
(d) 81
Ans. (b)

Ques. Matrix theory was introduced by
(a) Newton
(b) Cayley-Hamilton
(c) Cauchy
(d) Euclid
Ans. (b)

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Ques. If AB = C, then matrices A, B, C are
(a) A2×3, B3×2, C2×3
(b) A3×2, B2×3, C3×2
(c) A3×3, B2×3, C3×3
(d) A3×2, B2×3, C3×3
Ans. (d)

Ques. If A, B are square matrices of order 3, A is non- singular and AB = O, then B is a
(a) Null matrix
(b) Singular matrix
(c) Unit matrix
(d) Non- singular matrix
Ans. (a)

Ques. If | A | denotes the value of the determinant of the square matrix A of order 3, then | – 2A | =
(a) –8 | A |
(b) 8 | A |
(c) –2 | A |
(d) None of these
Ans. (a)

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Ques. Which one of the following is not true?
(a) Matrix addition is commutative
(b) Matrix addition is associative
(c) Matrix multiplication is commutative
(d) Matrix multiplication is associative
Ans. (c)

Ques. If A and B are square matrices of the same order, then
(a) (AB)’ = A’B’
(b) (AB)’ = B’A’
(c) AB = O; If | A | = 0 or | B | = 0
(d) AB = O; if A = I or B = I
Ans. (b)

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