1
GATE EE 2008
+1
-0.3
$$A$$ is $$m$$ $$x$$ $$n$$ full rank matrix with $$m > n$$ and $${\rm I}$$ is an identity matrix. Let matrix $${A^ + } = {\left( {{A^T}A} \right)^{ - 1}}{A^T}.$$ Then which one of the following statement is false?
A
$$A{A^ + }A = A$$
B
$${\left( {A{A^ + }} \right)^2} = A{A^ + }$$
C
$${A^ + }A = {\rm I}$$
D
$$A{A^ + }A = {A^ + }$$
2
GATE EE 2007
+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 $$n$$
3
GATE EE 2005
+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
4
GATE EE 2002
+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
$$300$$
EXAM MAP
Medical
NEET