1
GATE CSE 2010
MCQ (Single Correct Answer)
+2
-0.6
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
$$x = -4,\,\,y = 10$$
2
GATE CSE 2008
MCQ (Single Correct Answer)
+2
-0.6
How many of the following matrices have an eigen value $$1$$?
$$\left[ {\matrix{ 1 & 0 \cr 0 & 0 \cr } } \right],\,\,\left[ {\matrix{ 0 & 1 \cr 0 & 0 \cr } } \right],\,\,\left[ {\matrix{ 1 & { - 1} \cr 1 & 1 \cr } } \right]\,\,and\,\,\left[ {\matrix{ { - 1} & 0 \cr 1 & { - 1} \cr } } \right]$$
A
one
B
two
C
three
D
four
3
GATE CSE 2008
MCQ (Single Correct Answer)
+2
-0.6
If $$M$$ is a square matrix with a zero determinant, which of the following assertion(s) is (are) correct?
$$S1$$ : Each row of $$M$$ can be represented as a linear combination of the other rows
$$S2$$ : Each column of $$M$$ can be represented as a linear combination of the other columns
$$S3$$ : $$MX$$ $$=$$ $$0$$ has a nontrivial solution
$$S4$$ : $$M$$ has an inverse
A
$$S3$$ and $$S2$$
B
$$S1$$ and $$S4$$
C
$$S1$$ and $$S3$$
D
$$S1$$, $$S2$$, and $$S3$$
4
GATE CSE 2007
MCQ (Single Correct Answer)
+2
-0.6
Let $$A$$ be $$a$$ $$4$$ $$x$$ $$4$$ matrix with eigen values $$-5$$, $$-2, 1, 4$$.

Which of the following is an eigen value of $$\left[ {\matrix{ {\rm A} & {\rm I} \cr {\rm I} & {\rm A} \cr } } \right]$$, where $$I$$ is the $$4$$ $$x$$ $$4$$ identity matrix?

A
$$-5$$
B
$$-7$$
C
$$2$$
D
$$1$$
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