1
GATE IN 2010
MCQ (Single Correct Answer)
+1
-0.3
A real $$n \times n$$ matrix $$A$$ $$= \left[ {{a_{ij}}} \right]$$ is defined as
follows $$\left\{ {\matrix{ {{a_{ij}} = i,} & {\forall i = j} \cr { = 0,} & {otherwise} \cr } .} \right.$$

The sum of all $$n$$ eigen values of $$A$$ is

A
$${{n\left( {n + 1} \right)} \over 2}$$
B
$${{n\left( {n - 1} \right)} \over 2}$$
C
$${{n\left( {n + 1} \right)\left( {2n + 1} \right)} \over 2}$$
D
$${{n^2}}$$
2
GATE IN 2009
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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
$${\left[ {\matrix{ { - 2} & 1 \cr } } \right]^T}$$
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Medical
NEET
Graduate Aptitude Test in Engineering
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CBSE
Class 12