1
GATE CSE 2008
+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
2
GATE CSE 2008
+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 $$S3$$
3
GATE CSE 2007
+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
$$1$$
4
GATE CSE 2006
+2
-0.6
$$F$$ is an $$n$$ $$x$$ $$n$$ real matrix. $$b$$ is an $$n$$ $$x$$ $$1$$ real vector. Suppose there are two $$n$$ $$x$$ $$1$$ vectors, $$u$$ and $$v$$ such that $$u \ne v$$, and $$Fu = b,\,\,\,\,Fv = b$$

Which one of the following statements is false?

A
Dererminant of $$F$$ is zero
B
There are an infinite number of solutions to $$Fx$$ $$=$$ $$b$$
C
There is an $$x \ne 0$$ such that $$Fx = 0$$
D
$$F$$ must have two identical rows
GATE CSE Subjects
EXAM MAP
Medical
NEET