Find the least-square solution of Ax = b for | Mathematics II 2076

Mathematics II207610 marksNumerical: least squares solutionLeast squares problems

Find the least-square solution of $Ax = b$ for

$A = \begin{bmatrix} 1 & -6 \\ 1 & -2 \\ 1 & 1 \\ 1 & 7 \end{bmatrix} \text{ and } b = \begin{bmatrix} -1 \\ 2 \\ 1 \\ 6 \end{bmatrix}$

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Find the least-square solution of $Ax = b$ for

$$A = \begin{bmatrix} 1 & -6 \ 1 & -2 \ 1 & 1 \ 1 & 7 \end{bmatrix} \text{ and } b = \begin{bmatrix} -1 \ 2 \ 1 \ 6 \end{bmatrix}$$

[10]

$A = \begin{bmatrix} 1 & -6 \\ 1 & -2 \\ 1 & 1 \\ 1 & 7 \end{bmatrix}, \quad b = \begin{bmatrix} -1 \\ 2 \\ 1 \\ 6 \end{bmatrix}$ The least-square solution solves the normal equations: $A^T A \hat{x} = A^T b$ --- $A^T = \begin{bmatrix} 1 & 1 & 1 & 1 \\ -6 & -2 & 1 & 7 \end{bmatrix}$ -

$$A = \begin{bmatrix} 1 & -6 \ 1 & -2 \ 1 & 1 \ 1 & 7 \end{bmatrix}, \quad b = \begin{bmatrix} -1 \ 2 \ 1 \ 6 \end{bmatrix}$$ The least-square solution solves the normal equations: $$A^T A \hat{x} = A^T b$$ --- $$A^T = \begin{bmatrix} 1 & 1 & 1 & 1 \ -6 & -2 & 1 & 7 \end{bmatrix}$$ -

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