1
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
$$n$$
2
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
$${\left[ {\matrix{ { - 2} & 1 \cr } } \right]^T}$$
3
GATE IN 2005
+1
-0.3
Let $$A$$ be $$3 \times 3$$ matrix with rank $$2.$$ Then $$AX=O$$ has
A
only the trivial solution $$X=O$$
B
one independent solution
C
two independent solutions
D
three independent solutions
4
GATE IN 2001
+1
-0.3
The necessary condition to diagonalize a matrix is that
A
all its eigen values should be distinct
B
its eigen vectors should be independent
C
its eigen values should be real
D
the matrix is non-singular
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