Question

HELPPP!

Answer 1

Answer:

  c.  x ≈ 1.71, y ≈ 6.29, z ≈ 60.71

Step-by-step explanation:

You are at a bit of a disadvantage with this problem, because both the hint and the answer choices are incorrect.

The matrix equation is ...

$AX=B\\\\\left[\begin{array}{ccc}-1&1&0\\4&3&0\\1&-7&1\end{array}\right]\left[\begin{array}{c}x&y&z\end{array}\right]=\left[\begin{array}{c}8&12&15\end{array}\right]$

Contrary to what the hint is telling you, the multiplication by the inverse must be on the left:

$A^{-1}AX=A^{-1}B\\\\X=A^{-1}B$

Using appropriate tools to compute the inverse, this becomes ...

$\left[\begin{array}{c}x&y&z\end{array}\right]=\dfrac{1}{7}\left[\begin{array}{ccc}-3&1&0\\4&1&0\\31&6&7\end{array}\right]\left[\begin{array}{c}8&12&15\end{array}\right]\\\\\left[\begin{array}{c}x&y&z\end{array}\right]=\dfrac{1}{7}\left[\begin{array}{c}-12&44&425\end{array}\right]\approx\left[\begin{array}{c}-1.714&6.286&60.714\end{array}\right]$

The closest match is choice C.