\[\left| \begin{matrix} a & b & c \\ b & c & a \\ c & a & b... | MATH - EXPANSION OF DETERMINANTS, SOLUTION OF EQUATION | SolveeIt

Question

a & b & c \\ b & c & a \\ c & a & b \end{matrix} \right| =$$

$3abc + a^{3} + b^{3} + c^{3}$

$3abc - a^{3} - b^{3} - c^{3}$

$abc - a^{3} + b^{3} + c^{3}$

$abc + a^{3} - b^{3} - c^{3}$

Answer

$3abc - a^{3} - b^{3} - c^{3}$

Explanation

Solution

$\left| \begin{matrix} a & b & c \\ b & c & a \\ c & a & b \end{matrix} \right| = \left| \begin{matrix} a + b + c & a + b + c & a + b + c \\ b & c & a \\ c & a & b \end{matrix} \right|$ ,

$(R_{1} \rightarrow R_{1} + R_{2} + R_{3})$

= $(a + b + c)$ $k = 1, - 1.$

= $3abc - a^{3} - b^{3} - c^{3}$ , (After simplification).

Question: \[\left| \begin{matrix} a & b & c \\ b & c & a \\ c & a & b \end{matrix} \right| =\]...

Solution