1
GATE EE 2007
MCQ (Single Correct Answer)
+1
-0.3
$$X = {\left[ {\matrix{ {{x_1}} & {{x_2}} & {.......\,{x_n}} \cr } } \right]^T}$$ is an $$n$$-tuple non-
zero vector. The $$n\,\, \times \,\,n$$ matrix $$V = X{X^T}$$
A
has rank zero
B
has rank $$1$$
C
is orthogonal
D
has rank $$n$$
2
GATE EE 2005
MCQ (Single Correct Answer)
+1
-0.3
In the matrix equation $$PX=Q$$ which of the following is a necessary condition for the existence of atleast one solution for the unknown vector $$X.$$
A
Augmented matrix $$\left[ {P|Q} \right]$$ must have the same rank as matrix $$P.$$
B
vector $$Q$$ must have only non-zero elements.
C
matrix $$P$$ must be singular
D
matrix $$P$$ must be square
3
GATE EE 2002
MCQ (Single Correct Answer)
+1
-0.3
The determinant of the matrix $$\left[ {\matrix{ 1 & 0 & 0 & 0 \cr {100} & 1 & 0 & 0 \cr {100} & {200} & 1 & 0 \cr {100} & {200} & {300} & 1 \cr } } \right]$$ is
A
$$100$$
B
$$200$$
C
$$1$$
D
$$300$$
4
GATE EE 1999
MCQ (Single Correct Answer)
+1
-0.3
If $$A = \left[ {\matrix{ 1 & { - 2} & { - 1} \cr 2 & 3 & 1 \cr 0 & 5 & { - 2} \cr } } \right]$$ and $$adj (A)$$ $$ = \left[ {\matrix{ { - 11} & { - 9} & 1 \cr 4 & { - 2} & { - 3} \cr {10} & k & 7 \cr } } \right]$$ then $$k=$$
A
$$-5$$
B
$$3$$
C
$$-3$$
D
$$5$$
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