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
EXAM MAP
Medical
NEET