1
GATE ME 2015 Set 2
+1
-0.3
At least one eigenvalue of a singular matrix is
A
positive
B
zero
C
negative
D
imaginary
2
GATE ME 2015 Set 1
+1
-0.3
If any two columns of a determinant $$P = \left| {\matrix{ 4 & 7 & 8 \cr 3 & 1 & 5 \cr 9 & 6 & 2 \cr } } \right|$$ are interchanged, which one of the following statements regarding the value of the determinant is CORRECT?
A
absolute value remains unchanged but sign will change.
B
Both absolute valu and sign will change
C
Absolute value will change but sign will not change.
D
Both absolute value and sign will remain unchanged.
3
GATE ME 2014 Set 4
+1
-0.3
Which one of the following equations is a correct identity for arbitrary $$3 \times 3$$ real matrices $$P,Q$$ and $$R$$?
A
$$P(Q+R)=PQ+RP$$
B
$${\left( {P - Q} \right)^2} = {P^2} - 2PQ + {Q^2}$$
C
$$\det \,\,\left( {P + Q} \right) = \det \,P + \det \,Q$$
D
$${\left( {P + Q} \right)^2} = {P^2} + PQ + QP + {Q^2}$$
4
GATE ME 2014 Set 3
+1
-0.3
Consider a $$3 \times 3$$ real symmetric matrix $$S$$ such that two of its eigen values are $$a \ne 0,$$ $$b\,\, \ne 0$$ with respective eigen vectors $$\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr {{x_3}} \cr } } \right],\left[ {\matrix{ {{y_1}} \cr {{y_2}} \cr {{y_3}} \cr } } \right].$$ If $$a\, \ne b$$ then $${x_1}{y_1} + {x_2}{y_2} + {x_3}{y_3}$$ equals
A
$$a$$
B
$$b$$
C
$$ab$$
D
$$0$$
GATE ME Subjects
Engineering Mechanics
Machine Design
Strength of Materials
Heat Transfer
Production Engineering
Industrial Engineering
Turbo Machinery
Theory of Machines
Engineering Mathematics
Fluid Mechanics
Thermodynamics
General Aptitude
EXAM MAP
Joint Entrance Examination