1
GATE EE 2016 Set 1
MCQ (Single Correct Answer)
+2
-0.6
Let the eigenvalues of a $$2 \times 2$$ matrix $$A$$ be $$1,-2$$ with eigenvectors $${x_1}$$ and $${x_2}$$ respectively. Then the eigenvalues and eigenvectors of the matrix $${A^2} - 3A + 4{\rm I}$$ would respectively, be
A
$$2,14;{\,x_1},{x_2}$$
B
$$2,14;{x_1} + {x_2}:{x_1} - {x_2}$$
C
$$2,0;{\,x_1},{x_2}$$
D
$$2,0;\,{x_1} + {x_2},\,{x_1} - {x_2}$$
2
GATE EE 2016 Set 1
Numerical
+1
-0
Consider $$3 \times 3$$ matrix with every element being equal to $$1.$$ Its only non-zero eigenvalue is __________.
Your input ____
3
GATE EE 2016 Set 1
Numerical
+2
-0
Let $$\,\,S = \sum\limits_{n = 0}^\infty {n{\alpha ^n}} \,\,$$ where $$\,\,\left| \alpha \right| < 1.\,\,$$ The value of $$\alpha $$ in the range $$\,\,0 < \alpha < 1,\,\,$$ such that $$\,\,S = 2\alpha \,\,$$ is ___________.
Your input ____
4
GATE EE 2016 Set 1
Numerical
+1
-0
The maximum value attained by the function $$f(x)=x(x-1) (x-2)$$ in the interval $$\left[ {1,2} \right]$$ is _________.
Your input ____
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