1
GATE PI 2010
MCQ (Single Correct Answer)
+1
-0.3
If $$(1, 0, -1)$$$${}^T$$ is an eigen vector of the following matrix $$\left[ {\matrix{ 1 & { - 1} & 0 \cr { - 1} & 2 & { - 1} \cr 0 & { - 1} & 1 \cr } } \right]$$ then the corresponding eigen value is
A
$$1$$
B
$$2$$
C
$$3$$
D
$$5$$
2
GATE PI 2009
MCQ (Single Correct Answer)
+1
-0.3
The value of the determinant $$\left| {\matrix{ 1 & 3 & 2 \cr 4 & 1 & 1 \cr 2 & 1 & 3 \cr } } \right|$$ is
A
$$-28$$
B
$$-24$$
C
$$32$$
D
$$36$$
3
GATE PI 2007
MCQ (Single Correct Answer)
+1
-0.3
If $$A$$ is square symmetric real valued matrix of dimension $$2n$$, then the eigen values of $$A$$ are
A
$$2n$$ distinct real values
B
$$2n$$ real values not neccessarily distinct
C
$$n$$ distinct pairs of complex conjugate numbers
D
$$n$$ pairs of complex conjugate numbers, not necessarily distinct
4
GATE PI 2007
MCQ (Single Correct Answer)
+1
-0.3
The determinant $$\left| {\matrix{ {1 + b} & b & 1 \cr b & {1 + b} & 1 \cr 1 & {2b} & 1 \cr } } \right|$$ equals to
A
$$0$$
B
$$2b(b-1)$$
C
$$2(1-b)(1+2b)$$
D
$$3b(1+b)$$
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