GATE ME 2015 Set 1 | Linear Algebra Question 11 | Engineering Mathematics

GATE ME 2015 Set 1

MCQ (Single Correct Answer)

-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?

absolute value remains unchanged but sign will change.

Both absolute valu and sign will change

Absolute value will change but sign will not change.

Both absolute value and sign will remain unchanged.

GATE ME 2014 Set 1

MCQ (Single Correct Answer)

-0.3

Given that the determinant of the matrix $$\left[ {\matrix{ 1 & 3 & 0 \cr 2 & 6 & 4 \cr { - 1} & 0 & 2 \cr } } \right]$$ is $$-12$$, the determinant of the matrix $$\left[ {\matrix{ 2 & 6 & 0 \cr 4 & {12} & 8 \cr { - 2} & 0 & 4 \cr } } \right]$$ is

$$-96$$

$$-24$$

$$24$$

$$96$$

GATE ME 2014 Set 1

MCQ (Single Correct Answer)

-0.3

Which one of the following describes the relationship among the three vectors, $$\widehat i + \widehat j + \widehat k,\,\,2\widehat i + 3\widehat j + \widehat k$$ and $$5\widehat i + 6\widehat j + 4\widehat k?$$

The vectors are mutually perpendicular

The vectors are linearly dependent

The vectors are linearly independent

The vectors are unit vectors

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 $$R$$?

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

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

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

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