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Let A, B, and C be n×n matrices of the form A= [c_1...x...c_n], B= [c_1...y...c_n], and...

Let A, B, and C be n×n matrices of the form A= [c_1...x...c_n], B= [c_1...y...c_n], and C= [c_1...x+y...c_n] where x, y, and x+y are the jth column vectors. Use cofactor expansions to prove that det(C)=det(A)+det(B).

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Answer #1

Doubt or confusion in any step then comment below.. i will explain you.

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please thumbs up for this solution...thanks..

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Cof(C_i,j) represent cofactor of ith element of jth column

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Here we pick jth column ...and expand determinant about this column..

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