1
GATE CSE 2013
+1
-0.3
Which of the following does not equal
$$\left| {\matrix{ 1 & x & {{x^2}} \cr 1 & y & {{y^2}} \cr 1 & z & {{z^2}} \cr } } \right|?$$
A
$$\left| {\matrix{ 1 & {x\left( {x + 1} \right)} & {x + 1} \cr 1 & {y\left( {y + 1} \right)} & {y + 1} \cr 1 & {z\left( {z + 1} \right)} & {z + 1} \cr } } \right|$$
B
$$\left| {\matrix{ 1 & {x + 1} & {{x^2} + 1} \cr 1 & {y + 1} & {{y^2} + 1} \cr 1 & {z + 1} & {{z^2} + 1} \cr } } \right|$$
C
$$\left| {\matrix{ 0 & {x - y} & {{x^2} - {y^2}} \cr 0 & {y - z} & {{x^2} - {z^2}} \cr 1 & z & {{z^2}} \cr } } \right|$$
D
$$\left| {\matrix{ 2 & {x + y} & {{x^2} + {y^2}} \cr 2 & {y + z} & {{x^2} + {z^2}} \cr 1 & z & {{z^2}} \cr } } \right|$$
2
GATE CSE 2012
+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 $$-512\sqrt 2$$
3
GATE CSE 2010
+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
$$x=-4,$$ $$y=10$$
4
GATE CSE 2008
+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
GATE CSE Subjects
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