IIT-JEE 2012 · Paper 1 · Mathematics Q47

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MathematicsSingle correct+3 / -1Question 47 of 60

Let $P=[a_{ij}]$ be a $3\times3$ matrix and let $Q=[b_{ij}]$ , where $b_{ij}=2^{i+j}a_{ij}$ for $1\le i,j\le3$ . If the determinant of $P$ is 2, then the determinant of the matrix $Q$ is

2^{10}

2^{11}

2^{12}

2^{13}

Answer and worked solution

Official answer: D

Factor out the powers of 2. $b_{ij}=2^i\cdot2^j\cdot a_{ij}$ . Taking $2^i$ out of row $i$ and $2^j$ out of column $j$ :
$\det Q=2^{1+2+3}\cdot2^{1+2+3}\cdot\det P=2^{12}\cdot2=2^{13}.$

(D)

Topics:Determinants and properties

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IIT-JEE 2012 · Paper 1, Mathematics question 47