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Solve the equation $ \begin{vmatrix} x+a & x & x \\ x & x+a & x\\ x & x & x+a \end{vmatrix}=0, \; a \neq 0. $

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  • Determinants of a matrix of order three can be determined by expressing it in terms of second order determinants .This is known as expression of a determinant along a row or a column.
Solve for $x=\begin{vmatrix}x+a & x & x\\x & x+a & x\\x & x & x+a\end{vmatrix}=0$
Now expanding along $R_1$ we get,
On simplifying we get,
On simplifying further
$\Rightarrow x(a^2+2a^2)+a^3=0.$
Hence $x=\frac{-a}{3}.$
answered Mar 1, 2013 by balaji.thirumalai

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