1
GATE IN 2010
+1
-0.3
$$X$$ and $$Y$$ are non-zero square matrices of size $$n \times n$$. If $$XY = {O_{n \times n}}$$ then
A
$$\left| X \right| = 0\,$$ and $$\,\left| Y \right| \ne 0$$
B
$$\left| X \right| \ne 0\,$$ and $$\,\left| Y \right| = 0$$
C
$$\left| X \right| = 0$$ and $$\,\left| Y \right| = 0$$
D
$$\left| X \right| \ne 0$$ and $$\,\left| Y \right| \ne 0$$
2
GATE IN 2009
+1
-0.3
The eigen values of a $$2 \times 2$$ matrix $$X$$ are $$-2$$ and $$-3$$. The eigen values of matrix $${\left( {X + 1} \right)^{ - 1}}\left( {X + 5{\rm I}} \right)$$ are
A
$$-3, -4$$
B
$$-1, -2$$
C
$$-1, -3$$
D
$$-2, -4$$
3
GATE IN 2007
+1
-0.3
Let $$A = \left[ {{a_{ij}}} \right],\,\,1 \le i,j \le n$$ with $$n \ge 3$$ and
$${{a_{ij}} = i.j.}$$ Then the rank of $$A$$ is
A
$$0$$
B
$$-1$$
C
$$n-1$$
D
$$n$$
4
GATE IN 2005
+1
-0.3
Identity which one of the following is an eigen vectors of the matrix $$A = \left[ {\matrix{ 1 & 0 \cr { - 1} & { - 2} \cr } } \right]$$
A
$${\left[ {\matrix{ { - 1} & 1 \cr } } \right]^T}$$
B
$${\left[ {\matrix{ { 3} & -1 \cr } } \right]^T}$$
C
$${\left[ {\matrix{ { 1} & -1 \cr } } \right]^T}$$
D
$${\left[ {\matrix{ { - 2} & 1 \cr } } \right]^T}$$
GATE IN Subjects
EXAM MAP
Medical
NEET