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Question
Show that `|(x + 2"a", y + 2"b", z + 2"c"),(x, y, z),("a", "b", "c")|` = 0
Solution
Let Δ = `|(x + 2"a", y + 2"b", z + 2"c"),(x, y, z),("a", "b", "c")|`
Δ = `2/2 |(x + 2"a", y + 2"b", z + 2"c"),(x, y, z),("a", "b", "c")|`
= `1/2 |(x + 2"a", y + 2"b", z + 2"c"),(x, y, z),(2"a", 2"b", 2"c")|`
= `1/2 |(x + 2"a", y + 2"b", z + 2"c"),(x + 2"a", y + 2"b", z + 2"c"),(2"a", 2"b", 2"c")| "R"_2 -> "R"_2 + "R"_3`
= `1/2 xx 0`
= 0
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