Prove that `|{:(1, " "1, " "1), (1, 1+x, " "1), (1, " "1, 1+y):}|=xy.` – InterviewSolution

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1.	Prove that `\|{:(1, " "1, " "1), (1, 1+x, " "1), (1, " "1, 1+y):}\|=xy.`
Answer» The given determinant `=\|{:(1, " "1, " "1), (1, 1+x, " "1), (1, " "1, 1+y):}\|` `=\|{:(1, 0, 0), (1, x, 0), (1, 0, y):}\|" "["applying"C_(2) to C_(2)-C_(1) " and "C_(3) to C_(3)-C_(1)]` ` = 1 * \|{:(x, 0), (0, y):}\| = xy " "["expanding by "R_(1)].`

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