Use Gaussian elimination to solve each of the following systems of equations: a ) ? ? ? 3 ? 1 1...

Question:

Use Gaussian elimination to solve each of the following systems of equations:

{eq}a) \begin{bmatrix} 3 & -1 & 1 & 0 \\ 2 & 4& 0& -2\\ 0 & -7& 1& 3\end{bmatrix}\begin{bmatrix} x\\ y\\ z\\ w \end{bmatrix}=\begin{bmatrix} 0\\ 2\\ -3 \end{bmatrix} \\ b) \begin{bmatrix} 2 & -2 & 6\\ 2 & -1 & 2\\ 1 & 0& -1 \end{bmatrix}\begin{bmatrix} x\\ y\\ z \end{bmatrix}=\begin{bmatrix} 0\\ 0\\ 0 \end{bmatrix} {/eq}

Gaussian Elimination:

The Gaussian elimination method is used to find the solution of the given system of linear equations. The row operations are used in the Gaussian elimination method to solve the system of linear equations.

Answer and Explanation: 1

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a)

We have,

{eq}\begin{bmatrix} 3 & -1 & 1 & 0 \\ 2 & 4& 0& -2\\ 0 & -7& 1& 3 \end{bmatrix}...

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How to Solve Linear Systems Using Gaussian Elimination

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Chapter 10 / Lesson 6
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Learn about Gaussian elimination, one of the methods of solving a system of linear equations. Understand how to do Gaussian elimination with the help of an example.


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