1
GATE EE 2015 Set 2
+1
-0.3
We have a set of $$3$$ linear equations in $$3$$ unknown. $$'X \equiv Y'$$ means $$X$$ and $$Y$$ are equivalent statements and $$'X \ne Y'$$ means $$X$$ and $$y$$ are not equivalent statements.

$$P:$$ There is a unique solution.
$$Q:$$ The equations are linearly independent .
$$R:$$ All eigen values of the coefficient matrix are non zero .
$$S:$$ The determinant of the coefficient matrix is non-zero .

Which one of the following is TRUE?
A
$$P \equiv Q \equiv R \equiv S$$
B
$$P \equiv R \ne Q \equiv S$$
C
$$P \equiv Q \ne R \equiv S$$
D
$$P \ne Q \ne R \ne S$$
2
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 $${b_2}$$
3
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
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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