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Q.
Let P=[aij] be a 3×3 matrix and let Q=[bij] where bij=2i+jaij for 1≤i,j≤3.If the determinant of P is 2, then the determinant of the matrix Q is
IIT JEEIIT JEE 2012Determinants
Solution:
Plan It is a simple question on scalar multiplication, i.e |ka1ka2ka3b1b2b3c1c2c3|=k|a1a2a3b1b2b3c1c2c3|
Description of Situation Construction of matrix,
i.e. if a=[aij]3×3=[a11a12a13a21a22a23a31a32a33]
Here, P=[aij]3×3=[a11a12a13a21a22a23a31a32a33] Q=[bij]3×3=[b11b12b13b21b22b23b31b32b33]
where, bij=2i+jaij ∴|Q|=[4a118a1216a138a2116a2232a2316a3132a3264a33] =4×8×16[a11a12a132a212a222a234a314a324a33] =29×2×4[a11a12a13a21a22a23a31a32a33]=212⋅|P|=212⋅2=21,3