Question

Write a matrix equation to solve for the variables. Write your solution as an ordered triple (x,y,z).
x+y-z=14
4x-y+5z=-22
2x+2y-3z=35

Answer 1

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Answer 2

\[
\left[\begin{matrix}
1&1&-1\\
4&-1&5\\
2&2&-3
\end{matrix}\right]\cdot
\left[\begin{matrix}
x\\y\\z
\end{matrix}\right]=
\left[\begin{matrix}
14\\-22\\35
\end{matrix}\right]\\
\text{We can create an augmented matrix:}\\
\left[\begin{array}{ccc|c}
1&1&-1&14\\
4&-1&5&-22\\
2&2&-3&35
\end{array}\right]\\
\text{Then use elimination:}\\
\left[\begin{array}{ccc|c}
1&1&-1&14\\
0&-5&9&-78\\
0&0&-1&7
\end{array}\right]\\
\left[\begin{array}{ccc|c}
1&1&0&7\\
0&-5&0&-15\\
0&0&1&-7
\end{array}\right]\\
\left[\begin{array}{ccc|c}
1&0&0&4\\
0&1&0&3\\
0&0&1&-7
\end{array}\right]\\
\text{And we have our result: }(4,3,-7)
\]

Answer 3

I WATCHED TE MATRIX just find neo