91Ó°ÊÓ

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

In Exercises \(I-3,\) let \(\mathbf{u}=\left[\begin{array}{r}-1 \\ 4 \\\ -5\end{array}\right]\) 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 \(\mathbf{u}\)

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. $$y=-3+2 x$$

$$\text { let } \mathbf{u}=\left[\begin{array}{r}2 \\\\-1\end{array}\right] \text { and } \mathbf{v}=\left[\begin{array}{l}3 \\\4\end{array}\right]$$ \(\langle\mathbf{u}, \mathbf{v}\rangle\) is the inner product of Example 7.3 with \(A=\left[\begin{array}{rr}4 & -2 \\ -2 & 7\end{array}\right] .\) Compute (a) \(\langle\mathbf{u}, \mathbf{v})\) (b) \(\|\mathbf{u}\|\) \((c) d(\mathbf{u}, \mathbf{v})\)

Find the singular values of the given matrix. $$A=\left[\begin{array}{ll} 3 & 1 \\ 1 & 3 \end{array}\right]$$

In Exercises \(I-3,\) let \(\mathbf{u}=\left[\begin{array}{r}-1 \\ 4 \\\ -5\end{array}\right]\) 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 best linear approximation to fon the interval [-1,1]. $$f(x)=x^{2}+2 x$$

Find the best linear approximation to f on the interval [-1,1]. $$f(x)=x^{3}$$

Find the singular values of the given matrix. $$A=\left[\begin{array}{ll} 1 & 1 \\ 0 & 0 \end{array}\right]$$