1
GATE ECE 2018
MCQ (Single Correct Answer)
+1
-0.33
Let M be a real 4 $$\times$$ 4 matrix. Consider the following statements :

S1: M has 4 linearly independent eigenvectors.

S2: M has 4 distinct eigenvalues.

S3: M is non-singular (invertible).

Which one among the following is TRUE?
A
S1 implies S2
B
S2 implies S1
C
S1 implies S3
D
S3 implies S2
2
GATE ECE 2018
Numerical
+1
-0.33
Consider matrix $$A = \left[ {\matrix{ k & {2k} \cr {{k^2} - k} & {{k^2}} \cr } } \right]$$ and

vector $$X = \left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right]$$.

The number of distinct real values of k for which the equation AX = 0 has infinitely many solutions is _______.
3
GATE ECE 2017 Set 1
MCQ (Single Correct Answer)
+1
-0.3
The rank of the matrix $$M = \left[ {\matrix{ 5 & {10} & {10} \cr 1 & 0 & 2 \cr 3 & 6 & 6 \cr } } \right]$$ is
A
$$0$$
B
$$1$$
C
$$2$$
D
$$3$$
4
GATE ECE 2017 Set 1
MCQ (Single Correct Answer)
+1
-0.3
Consider the $$5 \times 5$$ matrix $$A = \left[ {\matrix{ 1 & 2 & 3 & 4 & 5 \cr 5 & 1 & 2 & 3 & 4 \cr 4 & 5 & 1 & 2 & 3 \cr 3 & 4 & 5 & 1 & 2 \cr 2 & 3 & 4 & 5 & 1 \cr } } \right]$$
It is given that $$A$$ has only one real eigen value. Then the real eigen value of $$A$$ is
A
$$-2.5$$
B
$$0$$
C
$$15$$
D
$$25$$
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