1
GATE CSE 2011
MCQ (Single Correct Answer)
+2
-0.6
Consider the matrix as given below. $$$\left[ {\matrix{ 1 & 2 & 3 \cr 0 & 4 & 7 \cr 0 & 0 & 3 \cr } } \right]$$$

Which of the following options provides the Correct values of the Eigen values of the matrix?

A
$$1, 4, 3$$
B
$$3, 7, 3$$
C
$$7, 3, 2$$
D
$$1, 2, 3$$
2
GATE CSE 2011
MCQ (Single Correct Answer)
+2
-0.6
$$\left[ A \right]$$ is a square matrix which is neither symmetric nor skew-symmetric and $${\left[ A \right]^T}$$ is its transpose. The sum and differences of these matrices and defined as $$\left[ S \right] = \left[ A \right] + {\left[ A \right]^T}$$ and $$\left[ D \right] = \left[ A \right] - {\left[ A \right]^T}$$ respectively. Which of the following statements is true?
A
Both $$\left[ S \right]$$ and $$\left[ D \right]$$ are symmetric
B
Both $$\left[ S \right]$$ and $$\left[ D \right]$$ are skew-symmetric
C
$$\left[ S \right]$$ is skew-symmetric and $$\left[ D \right]$$ is symmetric
D
$$\left[ S \right]$$ is symmetric and $$\left[ D \right]$$ is skew symmetric
3
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
$$x = -4,\,\,y = 10$$
4
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
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