MathAlgebraLinear algebraMatrix decomposition

Least squares

Assessing the error

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Consider the least squares problem with:X=(121112130101)y=(2032)X= \begin{pmatrix} 1 & -2 & 1 \\ 1 & 1 & 2 \\ 1 & 3 & 0 \\ 1 & 0 & 1 \\ \end{pmatrix} \qquad \mathbf{y}= \begin{pmatrix} -2 \\ 0 \\ 3 \\ 2\end{pmatrix}The pseudoinverse is given by:

X=122(1310127533151481)X^{\dag}= \frac{1}{22} \begin{pmatrix} 13 & -10 & 12 & 7 \\ -5 & 3 & 3 & -1 \\ -5 & 14 & -8 & -1 \\ \end{pmatrix}Compute the error with two decimal places

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