Q.

Let P=aij be a 3X3 matrix and let Q=bij where bij=2i+jaij for1≤i,j≤3. If the determinant of P is 2, then the determinant of Q is

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a

210

b

211

c

212

d

213

answer is D.

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Detailed Solution

We haveQ=22a1123a1224a1323a2124a2225a2324a3125a3226a33∴|Q|=22·23·24a112a1222a13a212a2222a23a312a3222a33⇒|Q|=212a11a12a13a21a22a23a31a32a33=212|P|=213   ∵|P|=2
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Let P=aij be a 3X3 matrix and let Q=bij where bij=2i+jaij for1≤i,j≤3. If the determinant of P is 2, then the determinant of Q is