Question

x + 2y - 4z = 2

2x + 6y + 6z = - 12

5x + y + 4z = -5 (Solving systems of equation w/ 3 variables)

Answer 1

use matrices to solve bhis equation

Answer 2

\[\left[\begin{matrix}1 & 2 & -4\\2 & 6 & 6 \\ 5 & 1 & 4\end{matrix}\right]\left(\begin{matrix}x \\ y\\z\end{matrix}\right) = \left(\begin{matrix}2\\ -12\\-5\end{matrix}\right)\]
Let Au=B
A = \[\left[\begin{matrix}1 & 2 & -4\\2 & 6 & 6 \\ 5 & 1 & 4\end{matrix}\right]\]
u=\[\left(\begin{matrix}x \\y\\ z\end{matrix}\right)\]
B = \[\left(\begin{matrix}2 \\-12\\ -5\end{matrix}\right)\]
\[\therefore u = A ^{-1} \times B\]

Answer 3

\[A ^{-1} \] = http://www.wolframalpha.com/input/?i= {{1%2C2%2C4}%2C{2%2C6%2C6}%2C{5%2C1%2C4}}
\[u =A^{-1} \times B\]
http://www.wolframalpha.com/input/?i= {{-9%2F25%2C+2%2F25%2C+6%2F25}%2C+{-11%2F25%2C+8%2F25%2C+-1%2F25}%2C+{14%2F25%2C+-9%2F50%2C+-1%2F25}}+*{{2}%2C{-12}%2C{-5}}
\[\therefore u = \left(\begin{matrix}{-72/25} \\ {-113/25}\\{87/25}\end{matrix}\right)\]