1
GATE ECE 2008
+1
-0.3
All the four entries of $$2$$ $$x$$ $$2$$ matrix
$$P = \left[ {\matrix{ {{p_{11}}} & {{p_{12}}} \cr {{p_{21}}} & {{p_{22}}} \cr } } \right]$$ are non-zero and one of the eigen values is zero. Which of the following statement is true?
A
$${P_{11}}\,{P_{22}} - {P_{12}}\,{P_{21}} = 1$$
B
$${P_{11}}\,{P_{22}} - {P_{12}}\,{P_{21}} = - 1$$
C
$${P_{11}}\,{P_{22}} - {P_{21}}\,{P_{12}} = 0$$
D
$${P_{11}}\,{P_{22}} + {P_{12}}\,{P_{21}} = 0$$
2
GATE ECE 2008
+1
-0.3
The system of linear equations $$\left. {\matrix{ {4x + 2y = 7} \cr {2x + y = 6} \cr } } \right\}$$ has
A
a unique solution
B
no solution
C
an infinite no. of solutions
D
exactly two distinct solution.
3
GATE ECE 2006
+1
-0.3
For the matrix $$\left[ {\matrix{ 4 & 2 \cr 2 & 4 \cr } } \right].$$ The eigen value corresponding to the eigen vector $$\left[ {\matrix{ {101} \cr {101} \cr } } \right]$$ is
A
$$2$$
B
$$4$$
C
$$6$$
D
$$8$$
4
GATE ECE 2006
+1
-0.3
The rank of the matrix $$\left[ {\matrix{ 1 & 1 & 1 \cr 1 & { - 1} & 0 \cr 1 & 1 & 1 \cr } } \right]$$ is
A
$$0$$
B
$$1$$
C
$$2$$
D
$$3$$
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