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Question

Let P=[aij] be a 3×3 matrix and let Q=[bij], where bij=2i+jaij. for 1i,j3. If the determinant of P is 2, then the determinant of the matrix Q is

A
210
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B
211
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C
212
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D
213
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Solution

The correct option is B 213
P(X)=∣ ∣a11a12a13a21a22a23a31a32a33∣ ∣

Q=[bij]=2i+jaij
Q=∣ ∣ ∣22a1123a1224a1323a2124a2225a2324a3125a3226a33∣ ∣ ∣
Taking 22,23,and24 common from 1st, 2nd and 3rd row respectively, we get
Q=29∣ ∣ ∣a112a1222a13a212a2222a23a312a3222a33∣ ∣ ∣

Now taking 2,22 common from 2nd and 3rd column respectively, we get

Q=29×23∣ ∣a11a12a13a21a22a23a31a32a33∣ ∣
Q=29×23P=29×24 (|P|=2)

|Q|=213

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