[ASK/EM-I/MCQ] August 30, 2012 Engineering Mathematics –I MCQ for Phase-I UNIT: I – MATRICES 1. The rank of the matrix A = (a) 4 (b) 2 (c) 0 (d) 1 2. The value of λ for which the matrix A = will be of rank one is (a) λ = -3 (b) λ = 3 (c) λ = 2 (d) λ = -2 3. For what value of k is the rank of matrix equal to 2. A = (a)any row number (b) 1 (c) 3 (d) 2 4. A be the matrix of order m × n then the rank of matrix A is (a) rank A ≤ min. of m and n (b) rank A ≥ min. of m and n (c) rank A < min. of m and n (d) rank A = min. of m and n 5. A matrix ‘A’ has a nonzero minor r then (a) ρ(A)< r (b) ρ(A)≤r (c) ρ(A)> r (d) ρ(A) ≥ r 6. If A is a m×n matrix of rank r such that PAQ =, then (a) P & Q are singular matrices (b) P is non-singular & Q is singular matrix (c) both P & Q must be a non-singular matrices (d) P -1 = Q 7. The system of equations is said to be consistent if (i) ρ(A) = ρ(A:B) = n (ii) ρ(A:B) < n (a) Both (i) & (ii) are true (b) only (i) is true (c) (i) is true but (ii) is false (d) (i) is false but (ii) is true
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[ASK/EM-I/MCQ] August 30, 2012
Engineering Mathematics –I
MCQ for Phase-I
UNIT: I – MATRICES
1. The rank of the matrix A =
(a) 4 (b) 2 (c) 0 (d) 1
2. The value of λ for which the matrix A =
will be of rank one is
(a) λ = -3 (b) λ = 3 (c) λ = 2 (d) λ = -2
3. For what value of k is the rank of matrix equal to 2.
A =
(a)any row number (b) 1 (c) 3 (d) 2
4. A be the matrix of order m × n then the rank of matrix A is
(a) rank A ≤ min. of m and n (b) rank A ≥ min. of m and n
(c) rank A < min. of m and n (d) rank A = min. of m and n
5. A matrix ‘A’ has a nonzero minor r then
(a) ρ(A)< r (b) ρ(A)≤r (c) ρ(A)> r (d) ρ(A) ≥ r
6. If A is a m×n matrix of rank r such that PAQ =
, then
(a) P & Q are singular matrices
(b) P is non-singular & Q is singular matrix
(c) both P & Q must be a non-singular matrices
(d) P-1 = Q
7. The system of equations is said to be consistent if
(i) ρ(A) = ρ(A:B) = n (ii) ρ(A:B) < n
(a) Both (i) & (ii) are true (b) only (i) is true
(c) (i) is true but (ii) is false (d) (i) is false but (ii) is true
[ASK/EM-I/MCQ] August 30, 2012
8. The condition on λ for which the system of equations
, has a unique solution is
(a) λ ≠ -5 (b) λ ≠ 5 (c) λ = 5 (d) λ = -5
9. The eigen values of the matrix A =
is
(a) a, b, g (b) a, b, 0 (c) a, 0, 0 (d)a, b, c
10. If λ is an eigen value of matrix A, then the eigen value of A-1 is
(a)
(b) λ (c) λ-1 (d) λ+1
11. If A = [ aij] is a square matrix of order n , then trace of A is
(a) product of diagonal elements (b) sum of diagonal elements
(c) sum of row elements (d) sum of column elements