Prove that : \(\begin{vmatrix}1&a&b\\[0.3em]-a&1&c\\[0.3em]-b&-c&1\en – InterviewSolution

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1.

Prove that : \(\begin{vmatrix}1&a&b\\[0.3em]-a&1&c\\[0.3em]-b&-c&1\end{vmatrix}\) = 1 + a2 + b2 + c2

Answer»

\(\begin{vmatrix}1&a&b\\[0.3em]-a&1&c\\[0.3em]-b&-c&1\end{vmatrix}\) = 1(1 + c²) - a(- a + bc) + bc(ac + b)

= 1 + c² + a² – abc + abc + b²

= 1 + a² + b² + c² = R.H.S. Proved.

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