1
GATE CSE 2012
MCQ (Single Correct Answer)
+1
-0.3
Let $$A$$ be the $$2 \times 2$$ matrix with elements $${a_{11}} = {a_{12}} = {a_{21}} = + 1$$ and $${a_{22}} = - 1$$. Then the eigen values of the matrix $${A^{19}}$$ are
A
$$1024$$ and $$-1024$$
B
$$1024\sqrt 2 \,i$$ and $$- 1024\sqrt 2$$
C
$$4\sqrt 2$$ and $$-4\sqrt 2$$
D
$$512\sqrt 2$$ and $$-512\sqrt 2$$
2
GATE CSE 2010
MCQ (Single Correct Answer)
+1
-0.3
Consider the following matrix $$A = \left[ {\matrix{ 2 & 3 \cr x & y \cr } } \right].$$
If the eigen values of $$A$$ are $$4$$ and $$8$$ then
A
$$x=4, y=10$$
B
$$x=5,$$ $$y=8$$
C
$$x=-3,$$ $$y=9$$
D
$$x=-4,$$ $$y=10$$
3
GATE CSE 2008
MCQ (Single Correct Answer)
+1
-0.3
The following system of equations
$${x_1}\, + \,{x_2}\, + 2{x_3}\, = 1$$
$${x_1}\, + \,2 {x_2}\, + 3{x_3}\, = 2$$
$${x_1}\, + \,4{x_2}\, + a{x_3}\, = 4$$ has a unique solution. The only possible value (s) for $$\alpha$$ is/are
A
0
B
either 0 or 1
C
one of 0, 1 or - 1
D
any real number except 5
4
GATE CSE 2007
MCQ (Single Correct Answer)
+1
-0.3
Let $$A$$ be the matrix $$\left[ {\matrix{ 3 & 1 \cr 1 & 2 \cr } } \right]$$. What is the maximum value of $${x^T}Ax$$ where the maximum is taken over all $$x$$ that are the unit eigenvectors of $$A$$?
A
$$5$$
B
$${{5 + \sqrt 5 } \over 2}$$
C
$$3$$
D
$${{5 - \sqrt 5 } \over 2}$$
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