 # Construct the augmented matrix that corresponds to the following system of equations. 5+(8x)/5=y 4z−3(x−4y)=0 5x−y=3(x−6z) Lewis Harvey 2020-11-30 Answered
Construct the augmented matrix that corresponds to the following system of equations.
$5+\frac{8x}{5}=y$
4z−3(x−4y)=0
5x−y=3(x−6z)
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Step 1
We have the system of equations as
$5+\frac{8x}{5}=y$
$\left(\frac{8}{5}\right)x+\left(-1\right)y+\left(0\right)z=\left(-5\right)$...(1)
And,
4z-3(x-4y)=0
(-3)x+(12)y+(4)z=0...(2)
Also,
5x-y=3(x-6z)
5x-y-3x+18z=0
(2)x+(-1)y+(18)z=0...(3)
Step 2
From the given system of equations represented by equations (1),(2) and (3), we can construct the augmented matrix as
$\left[\begin{array}{cccc}\frac{8}{5}& -1& 0& -5\\ -3& 12& 4& 0\\ 2& -1& 18& 0\end{array}\right]$
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