The system of linear equations x + y + z  = 6, x + 2y + 3z =14 and 2x + 5y + λz =μ (λ, μ \(\in \) R) is consistent with unique solution if _________

(a)

λ = 8

(b)

λ = 8, μ ≠ 36

(c)

λ ≠ 8

(d)

none

Let A be a 3 \(\times\) 3 matrix and B its adjoint matrix If |B| = 64, then |A| = ___________

(a)

±2

(b)

±4

(c)

±8

(d)

±12

The system of linear equations x + y + z = 2, 2x + y - z = 3, 3x + 2y + kz = has a unique solution if __________

(a)

k ≠ 0

(b)

-1 < k < 1

(c)

-2 < k < 2

(d)

k = 0

If A is a matrix of order m \(\times\) n, then \(\rho\) (A) is _________

(a)

m

(b)

n

(c)

≤ min (m,n)

(d)

≥ min (m,n)

If \(\rho\) (A) = r then which of the following is correct?

(a)

all the minors of order n which do not vanish

(b)

'A' has at least one minor of order r which does not vanish and all higher order minors vanish

(c)

'A' has at least one (r + 1) order minor which vanish

(d)

all (r + 1) and higher order minors should not vanish