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Problem 1

Use Gauss-Jordan row reduction to solve the given systems of equation. We suggest doing some by hand and others using technology. \(x+y=4\) \(x-y=2\)

Expert verified

The given system of equations is:
$$
x+y=4 \\
x-y=2
$$
Using Gauss-Jordan row reduction, we find the reduced row echelon form (RREF) of the augmented matrix:
$$
\begin{bmatrix}
1 & 0 & | & 3\\
0 & 1 & | & 1
\end{bmatrix}
$$
Converting the RREF matrix back into a system of equations, we get the solution \(x = 3\) and \(y = 1\).

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