1
GATE CSE 2005
+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 $$-1$$ 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
+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
4
GATE CSE 2004
+2
-0.6
How many solutions does the following system of linear equations have?

- x + 5y = - 1
x - y = 2
x + 3y = 3
A
infinitely many
B
two distinct solutions
C
unique
D
None
GATE CSE Subjects
Discrete Mathematics
Programming Languages
Theory of Computation
Operating Systems
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Computer Organization
Database Management System
Data Structures
Computer Networks
Algorithms
Compiler Design
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