Question

Assume the matrix below is the augmented matrix corresponding to a system of equations with variables x, y, and z (in that order). What is the exact value of z? 11 1 13 0 1 1 12 0 0 1 11
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Answer 1

Answer:

The answer is below

Step-by-step explanation:

The question is not complete, but a similar question is attached and solved.

An augmented matrix is a matrix obtained by appending the columns of two given matrices. The augmented matrix can be represented as:

$\left[\begin{array}{ccc}2&5&3\\4&7&2\\6&9&4\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{c}-1\\10\\-6\end{array}\right] \\\\\\\left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}2&5&3\\4&7&2\\6&9&4\end{array}\right] ^{-1}\left[\begin{array}{c}-1\\10\\-6\end{array}\right]$

$\left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}-5/9&-7/18&11/18\\2/9&5/9&-4/9\\1/3&-2/3&1/3\end{array}\right] \left[\begin{array}{c}-1\\10\\-6\end{array}\right]\\\\\\\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}-7\\8\\-9\end{array}\right]$

z = -9