Using properties of determinants prove that:
[C3’ = 2C3]
[C1’ = C1 - C3]
[C1’ = C1 + C2]
[C1’ = C1/(a2 + b2 + c2)]
[transforming row and column]
[C1’ = C1 - C2 & C2’ = C2 - C3]
[C1’ = C1/(a - b) & C2’ = C2/(b - c)]
= (a2 + b2 + c2)(a - b)(b - c){0 + 0 - a(a + b) + c(b + c)} [expansion by first row]
= (a2 + b2 + c2)(a - b)(b - c){0 + 0 - a(a + b) + c(b + c)}
= (a2 + b2 + c2)(a - b)(b - c)( - a2 - ba + bc + c2)
= (a2 + b2 + c2)(a - b)(b - c){(c2 - a2) + b(c - a)}
= (a2 + b2 + c2)(a - b)(b - c)(c - a)(a + b + c)
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