1
GATE IN 2016
Numerical
+2
-0
Consider the matrix $$A = \left( {\matrix{
2 & 1 & 1 \cr
2 & 3 & 4 \cr
{ - 1} & { - 1} & { - 2} \cr
} } \right)$$ whose eigen values are $$1, -1$$ and $$3$$. Then trace of $$\left( {{A^3} - 3{A^2}} \right)$$ is ________.
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2
GATE IN 2013
MCQ (Single Correct Answer)
+2
-0.6
One pair of eigenvectors corresponding to the two eigen values of the matrix $$\left[ {\matrix{
0 & { - 1} \cr
1 & {0 - } \cr
} } \right]$$
3
GATE IN 2007
MCQ (Single Correct Answer)
+2
-0.6
Let $$A$$ be $$n \times n$$ real matrix such that $${A^2} = {\rm I}$$ and $$Y$$ be an $$n$$-diamensional vector. Then the linear system of equations $$Ax=y$$ has
4
GATE IN 2006
MCQ (Single Correct Answer)
+2
-0.6
For a given $$2x2$$ matrix $$A,$$ it is observved that $$A\left[ {\matrix{
1 \cr
{ - 1} \cr
} } \right] = - 1\left[ {\matrix{
1 \cr
{ - 1} \cr
} } \right]$$ and
$$A\left[ {\matrix{ 1 \cr { - 2} \cr } } \right] = - 2\left[ {\matrix{ 1 \cr { - 2} \cr } } \right]$$ then the matrix $$A$$ is
$$A\left[ {\matrix{ 1 \cr { - 2} \cr } } \right] = - 2\left[ {\matrix{ 1 \cr { - 2} \cr } } \right]$$ then the matrix $$A$$ is
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