Question

Find the determinant of $\left[\begin{array}{ccc}1&4&2\\2&-1&4\\-3&7&6\end{array}\right]$

Answer 1

Answer:

$\text {Determinant = } -108$

Step-by-step explanation:

$\text{Find the determinant of} \left[\begin{array}{ccc}1&4&2\\2&-1&4\\-3&7&6\end{array}\right]$

$\text {Determinant = } 1 \times \left|\begin{array}{ccc}-1&7\\4&7\end{array}\right| - 4 \times \left|\begin{array}{ccc}2&4\\-3&6\end{array}\right| + 2 \times \left|\begin{array}{ccc}2&-1\\-3&7\end{array}\right|$

$\text {Determinant = } 1((-1)(6) - (4)(7)) - 4((2)(6) - (4)(-3)) + (2)((2)(7) - (-1)(-3))$

$\text {Determinant = } -34 -96 + 22$

$\text {Determinant = } -108$