Mathematics II207810 marksNumerical: least squares solutionLeast squares problems
Find a least square solution of the inconsistent system Ax=b for
Find a least square solution of the inconsistent system $Ax=b$ for
$$A = \begin{bmatrix} -1 & 2 \ 2 & -3 \ -1 & 3 \end{bmatrix}, \quad b = \begin{bmatrix} 4 \ 2 \ 1 \end{bmatrix}$$
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$$A = \begin{bmatrix} -1 & 2 \ 2 & -3 \ -1 & 3 \end{bmatrix}, \qquad b = \begin{bmatrix} 4 \ 2 \ 1 \end{bmatrix}$$ Unknown: $\hat{x} = \begin{bmatrix} x1 \ x2 \end{bmatrix}$ The least square solution satisfies the normal equations: $$A^T A ,\hat{x} = A^T b$$ $$A^T = \begin{bmatrix} -1 & 2 &...