Exercise 7.5: Choose the correct answer

Matrices and Determinants (Mathematics)

Choose the correct or the most suitable answer from the given four alternatives.

(1) If a_ij = 1/2 (3i − 2j ) and A = [a _ij] _2×2 is 

Ans: (2)

Solution

(2) What must be the matrix X, if 

Ans: (1)

Solution

(3) Which one of the following is not true about the matrix 

(1) a scalar matrix 

(2) a diagonal matrix 

(3) an upper triangular matrix 

(4) a lower triangular matrix 

Ans: (2)

(4) If A and B are two matrices such that A + B and AB are both defined, then 

(1) A and B are two matrices not necessarily of same order 

(2) A and B are square matrices of same order 

(3) Number of columns of A is equal to the number of rows of B 

(4) A = B. 

Ans: (2)

Solution

(5) If A = , then for what value of λ, A² = O ? 

 (1) 0 

(2) ±1 

(3) - 1 

(4) 1 

Ans: (2)

Solution

(6) If  and ( A + B )² = A² + B² then the values of a and b are

(1) a = 4, b = 1 

(2) a = 1, b = 4 

(3) a = 0, b = 4 

(4) a = 2, b = 4

Ans: (2)

Solution

 (7) If  is a matrix satisfying the equation  AA^T = 9I, where I is 3 × 3 identity matrix, then the ordered pair (a, b) is equal to

 (1) (2, - 1) 

(2) (- 2, 1) 

(3) (2, 1) 

(4) (- 2, - 1)

Ans: (4)

Solution

(8) If A is a square matrix, then which of the following is not symmetric?

 (1) A + A^T 

(2) AA^T 

(3) A^TA 

(4) A − A^T

Ans: (4)

Solution

(9) If A and B are symmetric matrices of order n, where ( A ≠ B), then

 (1) A + B is skew-symmetric 

(2) A + B is symmetric

 (3) A + B is a diagonal matrix 

(4) A + B is a zero matrix

Ans: (2)

Solution

(10)  If A =  and if xy = 1, then det ( AA^T ) is equal to

(1) (a −1)² 

(2) (a² +1)² 

(3) a² −1 

(4) (a² −1)²

Ans: (4)

Solution

(11) The value of x, for which the matrix A =   is singular is

(1) 9 

(2) 8 

(3) 7 

(4) 6

Ans: (2)

Solution

(12) If the points (x, −2), (5, 2), (8,8) are collinear, then x is equal to

 (1) - 3 

(2) 1/3 

(3) 1 

(4) 3

Ans: (4)

Solution

(13) If   = abc/2 ≠ 0, then the area of the triangle whose vertices are  is

(1) 1/4 

(2) 1/4abc 

(3) 1/8

(4) 1/8 abc

Ans: (3)

Solution

(14) If the square of the matrix  is the unit matrix of order 2, then α, β and γ should satisfy the relation. 

(1) 1+ α² + βγ = 0 

(2) 1− α² − βγ = 0

 (3) 1− α² + βγ = 0 

 (4)  1+ α² − βγ = 0

Ans: (2)

Solution

 (15) If   is 

(1) ∆ 

(2) k∆ 

(3) 3k∆ 

(4) k³∆

Ans: (4)

Solution

(16) A root of the equation  = 0 is 

(1) 6 

(2) 3 

(3) 0 

(4) - 6

Ans: (3)

Solution

 (17) The value of the determinant of A =  is

(1) - 2abc 

(2) abc 

(3) 0 

(4) a² + b² + c²

Ans: (3)

Solution

 (18) If  x₁ , x₂ , x₃ as well as y₁ , y ₂ , y₃ are in geometric progression with the same common ratio, then the points (x₁ , y₁ ), (x₂ , y₂ ), (x₃ , y₃) are

(1)  vertices of an equilateral triangle

(2)  vertices of a right angled triangle

(3)  vertices of a right angled isosceles triangle

(4) collinear

Ans: (4)

Solution

(19)  If denotes the greatest integer less than or equal to the real number under consideration and  −1 ≤ x < 0, 0 ≤ y < 1, 1 ≤ z < 2 , then the value of the determinant  is

Ans: (1)

Solution

 (20) If a ≠ b, b, c satisfy  = 0, then abc = 

 (1) a + b + c 

(2) 0 

(3) b³ 

(4) ab + bc

Ans: (3)

Solution

(21) If , then B is given by 

 (1) B = 4A 

(2) B = − 4A 

(3) B = − A 

(4) B = 6A

Ans: (2)

Solution

(22) If A is skew-symmetric of order n and C is a column matrix of order n × 1, then C^TAC is

(1) an identity matrix of order n 

(2) an identity matrix of order 1

(3) a zero matrix of order 1 

(4) an identity matrix of order 2

Ans: (3)

Solution

(23) The matrix A satisfying the equation  is

Ans: (3)

Solution

(24) If A+ I = , then ( A+I )( A-I ) is equal to 

Ans: (1)

Solution

(25)  Let A and B be two symmetric matrices of same order. Then which one of the following statement is not true?

(1) A + B is a symmetric matrix 

(2) AB is a symmetric matrix

(3) AB = (BA)^T 

(4) A^TB = AB^T

Ans: (2)

Solution