1
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
What are the eigen values of the matrix $$P$$ given below? $$$P = \left( {\matrix{ a & 1 & 0 \cr 1 & a & 1 \cr 0 & 1 & a \cr } } \right)$$$
A
$$a,a - \sqrt {2,} a + \sqrt 2 $$
B
$$a,a,a$$
C
$$0,a,2a$$
D
$$ - a,2a,2a$$
2
GATE CSE 2005
MCQ (Single Correct Answer)
+2
-0.6
Consider the set $$H$$ of all $$3$$ $$X$$ $$3$$ matrices of the type $$$\left[ {\matrix{ a & f & e \cr 0 & b & d \cr 0 & 0 & c \cr } } \right]$$$

Where $$a, b, c, d, e$$ and $$f$$ are real numbers and $$abc$$ $$ \ne \,\,0$$. Under the matrix multiplication operation, the set $$H$$ is:

A
$$a$$ group
B
$$a$$ monoid but not $$a$$ group
C
$$a$$ semigroup but not $$a$$ monoid
D
neither $$a$$ group nor $$a$$ semigroup
3
GATE CSE 2005
MCQ (Single Correct Answer)
+2
-0.6
What are the eigen values of the following $$2x2$$ matrix? $$$\left[ {\matrix{ 2 & { - 1} \cr { - 4} & 5 \cr } } \right]$$$
A
$$-1$$ and $$1$$
B
$$1$$ and $$6$$
C
$$2$$ and $$5$$
D
$$4$$ and $$-1$$
4
GATE CSE 2005
MCQ (Single Correct Answer)
+2
-0.6
Consider the following system of equations in three real variables $$x1, x2$$ and $$x3$$ :
$$2x1 - x2 + 3x3 = 1$$
$$3x1 + 2x2 + 5x3 = 2$$
$$ - x1 + 4x2 + x3 = 3$$
This system of equations has
A
no solution
B
a unique solution
C
more than one but a finite number of solutions
D
an infinite number of solutions
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Class 12