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. 4.(5 marks) Consider the system of equations: AB = W Here B is...
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4.(5 marks) Consider the system of equations:
Afl=w E EM Here [3 is the vector on unknowns. To have some common notation, let the columns of A be u and v.
Suppose we are given that the least-squares approximate solution B to the system is a = [:1 = [fl- Use this to find the parameters r and s.
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<p><span class="eqneditor-formula" data-value="A{\bf \beta}={\bf w}\\ A^TA\beta =A^T{\bf w}\\ \begin{bmatrix}1&1&1\\-r&0&r\end{bmatrix}\begin{bmatrix}1&-r\\1&0\\1&r\end{bmatrix}\begin{bmatrix}1\\1\end{bmatrix}=\begin{bmatrix}1&1&1\\-r&0&r\end{bmatrix}\begin{bmatrix}r\\1\\s\end{bmatrix}\\ \begin{bmatrix} 3&0\\ 0&2r^2 \end{bmatrix}\begin{bmatrix}1\\1\end{bmatrix}=\begin{bmatrix}r+s+1\\rs-r^2\end{bmatrix}\\ \begin{bmatrix}3\\ 2r^2\end{bmatrix}=\begin{bmatrix}r+s+1\\rs-r^2 \end{bmatrix}"><span class="katex"><span class="katex-mathml"></span><span class="katex-html"><span class="base"><span class="strut" style="height:.8888799999999999em;vertical-align:-.19444em;"></span><span class="mord mathnormal">s</span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:.05278em;">se</span></span></span><span class="mspace" style="margin-right:.2777777777777778em;"></span><span class="mrel">s</span><span class="mspace" 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mtight">s</span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">sec</span></span><span class="vlist-r"><span class="vlist" style="height:.9500000000000004em;"><span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size3">s</span></span></span></span></span></span></span></p><p>sectetur adipiscing elit. Nam lacinia pulvinar tortor</p><p>sectetur adipisci</p><p>sectetur adipiscing elit. Nam lacin</p><p>sectetur adipiscing elit. Nam lacinia pulvinar</p><p>sectetur adipi</p><p>sectetur</p><p>sectetur adipiscing</p><p>sectetur adipiscing e</p><p>sectetur adipiscing elit. Nam lacini</p><p> </p><p> </p><p> </p>
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