Question

HELPPP!

Select the correct answer.
Solve this system of equations using the inverse of a matrix.

Answer 1

Answer: c. x ≈ 1.71, y ≈ 6.29, z ≈ 60.71

Step-by-step explanation: I got this correct on Edmentum.

Answer 2

c. x ≈ 1.71, y ≈ 6.29, z ≈ 60.71

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]=(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]=(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.