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Question
Evaluate: `|("a" + x, y, z),(x, "a" + y, z),(x, y, "a" + z)|`
Solution
We have `|("a" + x, y, z),(x, "a" + y, z),(x, y, "a" + z)|`
[Applying C1 → C1 + C2 + C3]
= `|("a" + x + y + z,y, z),("a" + x + y + z, "a" + y, z),("a" + x + y + z, y, "a" + z)|`
= `("a" + x + y + z)|(1, y, z),(1, "a" + y, z),(1, y, "a" + z)|`
[Applying R2 → R2 – R1 and R3 → R3 – R1]
= `("a" + x + y + z)|(1, y, z),(0, "a", 0),(0, 0, "a")|`
= `("a" + x +y + z)|("a", 0),(0, "a")|`
= a2(a + z + x + y)
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