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2 years ago

Please help me with this.

Mathematics

1 answer:

OLga [1]2 years ago

8 0

Swapping rows alters the sign of the determinant:

$\begin{vmatrix} x & y & z \\ -8 & 2 & -12 \\ u & v & w \end{vmatrix} = - \begin{vmatrix} x & y & z \\ u & v & w \\ -8 & 2 & -12 \end{vmatrix}$

Multiplying a single row by a scalar scales the determinant by the same amount:

$\begin{vmatrix} x & y & z \\ u & v & w \\ -8 & 2 & -12 \end{vmatrix} = -2 \begin{vmatrix} x & y & z \\ u & v & w \\ 4 & -1 & 6 \end{vmatrix}$

Then

$\begin{vmatrix} x & y & z \\ -8 & 2 & -12 \\ u & v & w \end{vmatrix} = -(-2) \begin{vmatrix} x & y & z \\ u & v & w \\ 4 & -1 & 6 \end{vmatrix} = 2\times(-6) = \boxed{-12}$

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