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Question
Evaluate `|(x, y, x+y),(y, x+y, x),(x+y, x, y)|`
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Solution
Applying C1 → C1 + C2 + C3, we get
Δ = `|(2(x + y),y,x+y),(2(x + y), x+y,x),(2(x + y),x,y)|`
Taking 2(x + y) common from C1, we get
= `2(x + y)[(1,y,x+y),(1,x+y,x),(1,x,y)]`
Applying R2 → R2 − R1 and R3 → R3 − R1, we get
= `2(x + y)[(1,y,x+y),(0,x,-y),(0,x-y,-x)]`
Expanding along C1, we get
= 2(x + y) [x(−x) − (−y) (x − y)]
= 2(x + y) [−x2 + xy − y2]
= −2(x + y) (x2 − xy + y2)
= −2(x3 + y3)
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