1
GATE EE 2015 Set 1
Numerical
+1
-0
If the sum of the diagonal elements of a $$2 \times 2$$ matrix is $$-6$$, then the maximum possible value of determinant of the matrix is ____________.
2
GATE EE 2014 Set 2
+1
-0.3
Which one of the following statements is true for all real symmetric matrices?
A
All the eigen values are real
B
All the eigen values are positive
C
All the eigen values are distinct
D
Sum of all the eigen values is zero
3
GATE EE 2014 Set 1
+1
-0.3
Given a system of equations $$x + 2y + 2z = {b_1}$$$$$5x + y + 3z = {b_2}$$$
Which of the following is true its solutions
A
The system has a unique solution for any given $${b_1}$$ and $${b_2}$$
B
The system will have infinitely many solutions for any given $${b_1}$$ and $${b_2}$$
C
Whether or not a solution exists depends on the given $${b_1}$$ and $${b_2}$$
D
The system would have no solution for any values of $${b_1}$$ and $${b_2}$$
4
GATE EE 2012
+1
-0.3
Given that $$A = \left[ {\matrix{ { - 5} & { - 3} \cr 2 & 0 \cr } } \right]$$ and $${\rm I} = \left[ {\matrix{ 1 & 0 \cr 0 & 1 \cr } } \right],$$ the value of $${A^3}$$ is
A
$$15A+12$$ $${\rm I}$$
B
$$19A+30$$ $${\rm I}$$
C
$$17A+15$$ $${\rm I}$$
D
$$17A+21$$ $${\rm I}$$
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