Find the QR factorization of the matrix beginbmatrix 2 & 1 3 & -1 endb | Mathematics II 2076

Mathematics II20765 marksNumerical: QR factorizationThe Gram-Schmidt process

Find the QR factorization of the matrix $\begin{bmatrix} 2 & 1 \\ 3 & -1 \end{bmatrix}$ [5]

Find the QR factorization of the matrix $\begin{bmatrix} 2 & 1 \ 3 & -1 \end{bmatrix}$ [5]

$A = \begin{bmatrix} 2 & 1 \\ 3 & -1 \end{bmatrix}$ Columns: $\mathbf{a1} = \begin{bmatrix} 2 \\ 3 \end{bmatrix}, \qquad \mathbf{a2} = \begin{bmatrix} 1 \\ -1 \end{bmatrix}$ Goal: find orthogonal $Q$ and upper-triangular $R$ with $A = QR$ . $$\mathbf{u1} = \mathbf{a1} = \begin{bmatrix} 2 \ 3 ...

$$A = \begin{bmatrix} 2 & 1 \ 3 & -1 \end{bmatrix}$$ Columns: $$\mathbf{a1} = \begin{bmatrix} 2 \ 3 \end{bmatrix}, \qquad \mathbf{a2} = \begin{bmatrix} 1 \ -1 \end{bmatrix}$$ Goal: find orthogonal $Q$ and upper-triangular $R$ with $A = QR$. $$\mathbf{u1} = \mathbf{a1} = \begin{bmatrix} 2 \ 3 ...

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Find the QR factorization of the matrix beginbmatrix 2 & 1 3 & -1 endbmatrix