Question

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

Answer 1

Answer:

$\text {Determinant = } 37$

Step-by-step explanation:

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

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

$\text {Determinant = } 2[(-3)(1) - (1)(2)] - (-1)[(4)(1) - (1)(1)] + (4)[(4)(2) - (-3)(1)]$

$\text {Determinant = } - 10 + 3 + 44$

$\text {Determinant = } 37$