### 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*, AA^{T} 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 x_{2} – x_{3} = 1, –x_{1} + 2x_{3} = –2, x_{1} – 2x_{2} = 3 is

(a) Zero

(b) One

(c) Two

(d) Infinite

Ans. (a)

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**Ques. **f *I * is a unit matrix, then 3*I* 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 3A^{3} + 2A^{2} + 5A + I = 0 then its inverse is

(a) –(3A^{2} + 2A + 5I)

(b) 3A^{2} + 2A + 5I

(c) 3A^{2} – 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 x_{1} – x_{2} + x_{3} = 2, 3x_{1} – x_{2} + 2x_{3} = –6 and 3x_{1} + x_{2} + x_{3} = –18 has

(a) No solution

(b) Exactly one solution

(c) Infinite solutions

(d) None of these

Ans. (c)

**Ques. **If A^{2} – 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) A^{2} + 2AB + B^{2}

(b) A^{2} + AB + BA + B^{2
}(c) A^{2} + 2BA + B^{2}

(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) A_{2×3}, B_{3×2}, C_{2×3}

(b) A_{3×2}, B_{2×3}, C_{3×2
}(c) A_{3×3}, B_{2×3}, C_{3×3}

(d) A_{3×2}, B_{2×3}, C_{3×3}

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 | – 2*A *| =

(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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