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  • Let P=[aij] be a 3 by 3 matrix and Q=[bij], where bij=2^(i+j) aij for 1 less than equal to i, j less than equal to 3 If Det P=2 , then Det Q is

Let P=[aij] be a 3 by 3 matrix and Q=[bij], where bij=2^(i+j) aij for 1 less than equal to i, j less than equal to 3 If Det P=2 , then Det Q is

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Solution:

             Rightarrow            Q=eginvmatrix 2^2a_11 &2^3a_12 &2^4a_13 \2^3a_21 &2^4a_22 &2^5a_23 \2^4a_31 &2^5a_32 &2^4a_33 endvmatrix

           Rightarrow             Q=2^9eginvmatrix a_11 &a_12 &a_13 \2a_21 &2a_22 &2a_23 \2^2a_31 &2^2a_32 &2^2a_33 endvmatrix=2^9 imes 22 imes 2^2 Det(P)=2^12cdot 2=2^13

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Deependra Verma

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