Question

Find the determinant of $\left[\begin{array}{ccc}a&h&g\\h&b&f\\g&f&c\end{array}\right]$

Answer 1

Answer:

$\text {Determinant = } abc + 2fgh- af^2 - ch^2 - bg^2$

Step-by-step explanation:

$\text{Find the determinant of} \left[\begin{array}{ccc}a&h&g\\h&b&f\\g&f&c\end{array}\right]$

$\text {Determinant = } a \times \left|\begin{array}{ccc}b&f\\f&c\end{array}\right| - h \times \left|\begin{array}{ccc}h&f\\g&c\end{array}\right| + g \times \left|\begin{array}{ccc}h&b\\g&f\end{array}\right|$

$\text {Determinant = } a(bc - f^2) - h(hc - fg) + g(hf -bg)$

$\text {Determinant = } abc - af^2 - ch^2 + fgh + fgh -bg^2$

$\text {Determinant = } abc + 2fgh- af^2 - ch^2 - bg^2$