Question

Solve the system using a matrix.
2x + 2y – z = 4
4x - 2y – 2z = 2
3x + 3y
4z - 4
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Answer 1

Answer:

Step-by-step explanation:

$\begin{bmatrix}2&2&-1\\4&-2&-2\\3&3&-4\end{bmatrix}*\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}4\\2\\-4 \end{bmatrix}\\\\\\\\\begin{bmatrix}2&2&-1\\4&-2&-2\\3&3&-4\end{bmatrix}^{-1}=\begin{bmatrix}\dfrac{7}{15}&\dfrac{1}{6} &\dfrac{1}{5}\\\dfrac{1}{3}&-\dfrac{1}{6}&0\\\dfrac{3}{5}&0&-\dfrac{2}{5}\end{bmatrix}$

$\begin{bmatrix}\dfrac{7}{15}&\dfrac{1}{6} &\dfrac{1}{5}\\\dfrac{1}{3}&-\dfrac{1}{6}&0\\\dfrac{3}{5}&0&-\dfrac{2}{5}\end{bmatrix}*\begin{bmatrix}2&2&-1\\4&-2&-2\\3&3&-4\end{bmatrix}*\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}\dfrac{7}{15}&\dfrac{1}{6} &\dfrac{1}{5}\\\dfrac{1}{3}&-\dfrac{1}{6}&0\\\dfrac{3}{5}&0&-\dfrac{2}{5}\end{bmatrix}*\begin{bmatrix}4\\2\\-4 \end{bmatrix}$

$\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}*\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}3\\1\\4 \end{bmatrix}$