91Ó°ÊÓ

$$\text {Let } \mathbf{u}=\left[\begin{array}{r}-1 \\\4 \\\\-5\end{array}\right] \text { and } \mathbf{v}=\left[\begin{array}{r}2 \\\\-2 \\\0\end{array}\right]$$ Compute the Euclidean norm, the sum norm, and the max norm of \(\mathbf{u}\)

Find the best linear approximation to fon the interval [-1,1] $$f(x)=x^{2}$$

Find the singular values of the given matrix. $$A=\left[\begin{array}{ll} 2 & 0 \\ 0 & 3 \end{array}\right]$$

Consider the data points \((1,0),(2,1),\) and \((3,5) .\) Compute the least squares error for the given line. In each case, plot the points and the line. $$y=-2+2 x$$

Consider the data points \((1,0),(2,1),\) and \((3,5) .\) Compute the least squares error for the given line. In each case, plot the points and the line. $$y=x$$

$$\text {Let } \mathbf{u}=\left[\begin{array}{r}-1 \\\4 \\\\-5\end{array}\right] \text { and } \mathbf{v}=\left[\begin{array}{r}2 \\\\-2 \\\0\end{array}\right]$$ Compute the Euclidean norm, the sum norm, and the \(\max\) norm of \(\mathbf{v}\).

Find the singular values of the given matrix. $$A=\left[\begin{array}{ll} 2 & 1 \\ 1 & 2 \end{array}\right]$$

Find the best linear approximation to fon the interval [-1,1] $$f(x)=x^{2}+2 x$$

Let \(\mathbf{u}=\left[\begin{array}{r}1 \\ -2\end{array}\right]\) and \(\mathbf{v}=\left[\begin{array}{l}4 \\ 3\end{array}\right]\). In Exercise \(1,\) find a nonzero vector orthogonal to \(\mathbf{u}\).

Consider the data points \((1,0),(2,1),\) and \((3,5) .\) Compute the least squares error for the given line. In each case, plot the points and the line. $$y=-3+\frac{5}{2} x$$