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$\left| {\,\begin{array}{*{20}{c}}{a - b - c}&{2a}&{2a}\\{2b}&{b - c - a}&{2b}\\{2c}&{2c}&{c - a - b}\end{array}\,} \right| = $
${(a + b + c)^2}$
${(a + b + c)^3}$
$(a + b + c)(ab + bc + ca)$
એકપણ નહી.
Solution
(b) $\left| {\,\begin{array}{*{20}{c}}{a – b – c}&{2a}&{2a}\\{2b}&{b – c – a}&{2b}\\{2c}&{2c}&{c – a – b}\end{array}\,} \right|$
= $\left| {\,\begin{array}{*{20}{c}}{ – \Sigma a}&0&{2a}\\{\Sigma a}&{ – \Sigma a}&{2b}\\0&{\Sigma a}&{c – a – b}\end{array}\,} \right|$ , $\left( \begin{array}{l}{C_1} \to {C_1} – {C_2}\\{C_2} \to {C_2} – {C_3}\end{array} \right)$
= ${(\Sigma a)^2}\,\left| {\,\begin{array}{*{20}{c}}{ – 1}&0&{2a}\\1&{ – 1}&{2b}\\1&1&{c – a – b}\end{array}\,} \right| = {(\Sigma a)^3}$, (on expansion)
= ${(a + b + c)^3}$.
