evaluate determinants. top row -4,5,15
2nd row 8,-7,16
3rd row -4,21,-2

Question

evaluate determinants. top row -4,5,15
                                       2nd row 8,-7,16
                                        3rd row -4,21,-2

unklerhaukus · Answer

$$ det\left[\begin{matrix}-4&5 &15 \ 8&-7&16\ -4&21 & -2\end{matrix}\right] $$
$$=-4((-7\times-2)-(16 \times21))-5((8\times-2)-(-4\times 16))+15((8\times21)-(-7 \times -4)$$
$$=3148$$

anonymous · Answer

Use expansion by minors along the top row, for instance.  Don't forget to flip the sign on the second term.$$-4\begin{vmatrix}-7 & 16 \ 21 & -2\end{vmatrix}-5\begin{vmatrix}-8 & 16 \ -4 & -2\end{vmatrix}+15\begin{vmatrix}8 & -7 \ -4 & 21\end{vmatrix}$$Now, you can evaluate the smaller determinants by the following formula, which you definitely should make an effort to be second nature.$$\begin{vmatrix}a & b \ c & d\end{vmatrix} = ad-bc$$