GATE ME 2014 Set 4 | Linear Algebra Question 23 | Engineering Mathematics

GATE ME 2014 Set 4

MCQ (Single Correct Answer)

-0.3

Which one of the following equations is a correct identity for arbitrary $$3 \times 3$$ real matrices $$P,Q$$ and $$R$$?

$$P(Q+R)=PQ+RP$$

$${\left( {P - Q} \right)^2} = {P^2} - 2PQ + {Q^2}$$

$$\det \,\,\left( {P + Q} \right) = \det \,P + \det \,Q$$

$${\left( {P + Q} \right)^2} = {P^2} + PQ + QP + {Q^2}$$

GATE ME 2013

MCQ (Single Correct Answer)

-0.3

The eigen values of a symmetric matrix are all

complex with non-zero positive imaginary part.

complex with non-zero negative imaginary part.

real

pure imaginary

GATE ME 2012

MCQ (Single Correct Answer)

-0.3

For the matrix $$A = \left[ {\matrix{ 5 & 3 \cr 1 & 3 \cr } } \right],$$ ONE of the normalized eigen vectors is given as

$$\left( {\matrix{ {{1 \over 2}} \cr {{{\sqrt 3 } \over 2}} \cr } } \right)$$

$$\left( {\matrix{ {{1 \over {\sqrt 2 }}} \cr {{{ - 1} \over {\sqrt 2 }}} \cr } } \right)$$

$$\left( {\matrix{ {{3 \over {\sqrt {10} }}} \cr {{{ - 1} \over {\sqrt {10} }}} \cr } } \right)$$

$$\left( {\matrix{ {{1 \over 5}} \cr {{2 \over {\sqrt 5 }}} \cr } } \right)$$

GATE ME 2011

MCQ (Single Correct Answer)

-0.3

Consider the following system of equations
$$2{x_1} + {x_2} + {x_3} = 0,\,\,{x_2} - {x_3} = 0$$ and $${x_1} + {x_2} = 0.$$
This system has

a unique solution

no solution

infinite number of solutions

five solutions

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