1
GATE IN 2017
+1
-0.3
The eigen values of the matrix $$A = \left[ {\matrix{ 1 & { - 1} & 5 \cr 0 & 5 & 6 \cr 0 & { - 6} & 5 \cr } } \right]$$ are
A
$$-1,5,6$$
B
$$1, - 5 \pm j6$$
C
$$1,5 \pm j6$$
D
$$1,5,5$$
2
GATE IN 2017
Numerical
+1
-0
If $$V$$ is a non-zero vector of dimension $$3 \times 1,$$ then the matrix $$\,A = V{V^T}$$ has a rank $$=$$ ________
3
GATE IN 2015
+1
-0.3
Let $$A$$ be an $$n \times n$$ matrix with rank $$r\left( {0 < r < n} \right).$$ Then $$AX=0$$ has $$p$$ independent solutions, where $$p$$ is
A
$$r$$
B
$$n$$
C
$$n-r$$
D
$$n+r$$
4
GATE IN 2014
+1
-0.3
A scalar valued function is defined as $$f\left( x \right){x^T}Ax + {b^T}x + c,$$ where $$A$$ is a symmetric positive definite matrix with dimension $$n \times n;$$ $$b$$ and $$x$$ are vectors of dimension $$n \times 1$$. The minimum value of $$f(x)$$ will occur when $$x$$ equals.
A
$${\left( {{A^T}A} \right)^{ - 1}}B$$
B
$$- {\left( {{A^T}A} \right)^{ - 1}}B$$
C
$$- \left( {{{{A^{ - 1}}B} \over 2}} \right)$$
D
$${{{A^{ - 1}}B} \over 2}$$
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