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Linear AlgebraHardOrthogonality & Least Squares

Orthogonality & Least Squares · Hard problem

A least-squares problem is solved via QRQR factorization: Rx=QTbR\mathbf x = Q^T\mathbf b with R=(123014002)R = \begin{pmatrix}1&2&3\\0&1&4\\0&0&2\end{pmatrix} and QTb=(3,4,12)Q^T\mathbf b = (3,4,12). Using back-substitution, find x1x_1 (the first entry of the least-squares solution x\mathbf x).