Using properties of determinants prove that:




[R2’ = R2 - R3]


[R2’ = R2/4]


[transforming row and column]


[R1’ = R1 - R2 & R2’ = R2 - R3]



[R1’ = R1/(a - b) & R2’ = R2/(b - c)]


[R1’ = R1 - R2]


[R1’ = R1/(a - c)]


= 4(a - b)(b - c)(a - c)(c2 - 2c + 1 - bc - c2 + 2c + 0 + bc + c2 - c2) [expansion by first row]


= 4(a - b)(b - c)(c - a)


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