40.4: Overdefined systems

Matrix Algebra with Computational Applications · LibreTexts

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    import numpy as np
import sympy as sym
sym.init_printing()

    We also learned solutions to overdefined systems (more equations than unknowns) often do not exist. However, we can estimate a solution using Least Squares fit.

    Consider the following system of equations:

    \[\begin{split}\begin{bmatrix}5&-2&2 \\ 4 & -3 &4 \\ 4& -6 &7 \\ 6 & 3 & -3\end{bmatrix}\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}=\begin{bmatrix}1\\2\\3\\-1\end{bmatrix}\end{split} \nonumber \]

    Do This

    Solve the above using LSF.

    #Put your answer to the above question here.

    This page titled 40.4: Overdefined systems was last modified on Sat, 17 Sep 2022 15:13:55 GMT and is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Dirk Colbry via source content that was edited to the style and standards of the LibreTexts platform.