1
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 $$=$$ ________
2
GATE IN 2015
MCQ (Single Correct Answer)
+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
$$n+r$$
3
GATE IN 2014
MCQ (Single Correct Answer)
+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
$${{{A^{ - 1}}B} \over 2}$$
4
GATE IN 2014
MCQ (Single Correct Answer)
+1
-0.3
For the matrix $$A$$ satisfying the equation given below, the eigen values are $$\left[ A \right]\left[ {\matrix{ 1 & 2 & 3 \cr 7 & 8 & 9 \cr 4 & 5 & 6 \cr } } \right] = \left[ {\matrix{ 1 & 2 & 3 \cr 4 & 5 & 6 \cr 7 & 8 & 9 \cr } } \right]$$\$
A
$$(1,-j,j)$$
B
$$(1,1,0)$$
C
$$(1,1,-1)$$
D
$$(1,0,0)$$
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EXAM MAP
Medical
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Graduate Aptitude Test in Engineering
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CBSE
Class 12