Find the least square solution of Ax = b where and compute the associa | Mathematics II 2080.1

Mathematics II2080.110 marksNumerical: least squares solutionLeast squares problems

Find the least square solution of $Ax = b$ where and compute the associated least square error.

$A = \begin{bmatrix} 1 & -3 & -3 \\ 1 & 5 & 1 \\ 1 & 7 & 2 \end{bmatrix}, \quad b = \begin{bmatrix} 5 \\ -3 \\ -5 \end{bmatrix}$

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Find the least square solution of $Ax = b$ where and compute the associated least square error.

$$A = \begin{bmatrix} 1 & -3 & -3 \ 1 & 5 & 1 \ 1 & 7 & 2 \end{bmatrix}, \quad b = \begin{bmatrix} 5 \ -3 \ -5 \end{bmatrix}$$

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$A = \begin{bmatrix} 1 & -3 & -3 \\ 1 & 5 & 1 \\ 1 & 7 & 2 \end{bmatrix}, \quad b = \begin{bmatrix} 5 \\ -3 \\ -5 \end{bmatrix}$ The least square solution solves the normal equation $A^TA\hat{x} = A^Tb$ . --- $A^T = \begin{bmatrix} 1 & 1 & 1 \\ -3 & 5 & 7 \\ -3 & 1 & 2 \end{bmatrix}$ $$A^TA = ...

$$A = \begin{bmatrix} 1 & -3 & -3 \ 1 & 5 & 1 \ 1 & 7 & 2 \end{bmatrix}, \quad b = \begin{bmatrix} 5 \ -3 \ -5 \end{bmatrix}$$ The least square solution solves the normal equation $A^TA\hat{x} = A^Tb$. --- $$A^T = \begin{bmatrix} 1 & 1 & 1 \ -3 & 5 & 7 \ -3 & 1 & 2 \end{bmatrix}$$ $$A^TA = ...

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Find the least square solution of Ax = b where and compute the associated least square error.