InterviewSolution
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InterviewSolution
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`|[1,bc,bc(b+c)],[1,ca,ca(c+a)],[1,ab,ab(a+b)]|=0` |
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Answer» The given determinant `=|{:(1, bc, a(b+c)), (1, ca, b(c+a)), (1, ab, c(a+b)):}|` `=|{:(1, bc, ab+bc+ca), (1, ca, ab+bc+ca), (1, ab, ab+bc+ca):}| " "["applying"C_(3) to C_(3) + C_(2)]` ` =(ab + bc +ca) * =|{:(1, bc, 1), (1, ca, 1), (1, ab, 1):}| " "["taking (ab+bc+ca) common from" C_(3)]` ` = (ab + bc+ca) xx 0 =0 " " [because C_(1)" and "C_(3) are identical"]. ` |
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