1
GATE EE 2016 Set 1
MCQ (Single Correct Answer)
+2
-0.6
Let $$A$$ be a $$4 \times 3$$ real matrix which rank$$2.$$ Which one of the following statement is TRUE?
A
Rank of AT is less than $$2$$
B
Rank of ATA is equal to $$2$$
C
Rank of ATA is greater than $$2$$
D
Rank of ATA can be any number between $$1$$ and $$3$$
2
GATE EE 2016 Set 1
MCQ (Single Correct Answer)
+2
-0.6
Let the eigenvalues of a $$2 \times 2$$ matrix $$A$$ be $$1,-2$$ with eigenvectors $${x_1}$$ and $${x_2}$$ respectively. Then the eigenvalues and eigenvectors of the matrix $${A^2} - 3A + 4{\rm I}$$ would respectively, be
A
$$2,14;{\,x_1},{x_2}$$
B
$$2,14;{x_1} + {x_2}:{x_1} - {x_2}$$
C
$$2,0;{\,x_1},{x_2}$$
D
$$2,0;\,{x_1} + {x_2},\,{x_1} - {x_2}$$
3
GATE EE 2015 Set 1
MCQ (Single Correct Answer)
+2
-0.6
The maximum value of $$'a'$$ such that the matrix $$\left[ {\matrix{ { - 3} & 0 & { - 2} \cr 1 & { - 1} & 0 \cr 0 & a & { - 2} \cr } } \right]$$ has three linearly independent real eigenvectors is
A
$${2 \over {3\sqrt 3 }}$$
B
$${1 \over {3\sqrt 3 }}$$
C
$${{1 + 2\sqrt 3 } \over {3\sqrt 3 }}$$
D
$${{1 + \sqrt 3 } \over {3\sqrt 3 }}$$
4
GATE EE 2014 Set 1
Numerical
+2
-0
A system matrix is given as follows $$$A = \left[ {\matrix{ 0 & 1 & { - 1} \cr { - 6} & { - 11} & 6 \cr { - 6} & { - 11} & 5 \cr } } \right].$$$

The absolute value of the ratio of the maximum eigenvalue to the minimum eigenvalue is ___________.

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