1
GATE CE 2017 Set 2
MCQ (Single Correct Answer)
+1
-0.3
Consider the following simultaneous equations (with $${c_1}$$ and $${c_2}$$ being constants): $$$3{x_1} + 2{x_2} = {c_1}$$$ $$$4{x_1} + {x_2} = {c_2}$$$

The characteristic equation for these simultaneous equation is

A
$${\lambda ^2} - 4\lambda - 5 = 0$$
B
$${\lambda ^2} 4\lambda + 5 = 0$$
C
$${\lambda ^2} + 4\lambda - 5 = 0$$
D
$${\lambda ^2} + 4\lambda + 5 = 0$$
2
GATE CE 2017 Set 1
MCQ (Single Correct Answer)
+1
-0.3
The matrix $$P$$ is the inverse of a matrix $$Q.$$ If $${\rm I}$$ denotes the identity matrix, which one of the following options is correct?
A
$$PQ = {\rm I}\,\,\,but\,\,\,QP \ne {\rm I}$$
B
$$QP = {\rm I}\,\,\,but\,\,\,PQ \ne {\rm I}$$
C
$$PQ = {\rm I}\,\,\,and\,\,\,QP = {\rm I}$$
D
$$PQ - QP = {\rm I}$$
3
GATE CE 2016 Set 1
MCQ (Single Correct Answer)
+1
-0.3
If the entries in each column of a square matrix $$M$$ add up to $$1$$, then an eigenvalue of $$M$$ is
A
$$4$$
B
$$3$$
C
$$2$$
D
$$1$$
4
GATE CE 2015 Set 1
Numerical
+1
-0
For what value of $$'p'$$ the following set of equations will have no solutions? $$$2x+3y=5$$$ $$$3x+py=10$$$
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