Exercises

01

Gram-Schmidt practice

Perform Gram-Schmidt to find an orthogonal basis of the subspace:

$$⟨\left(\begin{array}{c}2\\ 0\\ 1\\ 0\end{array}\right),\left(\begin{array}{c}0\\ 1\\ 1\\ 1\end{array}\right),\left(\begin{array}{c}2\\ 2\\ 3\\ 2\end{array}\right)⟩.$$

02

Computing a best fit line

Following the steps above, compute the best fine line (i.e. compute $m$ and $b$) for the data used in Problem 05-03:

$$(-3,4),(1,-1),(0,-1),(4,-3),(-2,1).$$

In Problem 05-03, you already found $\bar{x}$ and $\bar{y}$, and implicitly $\hat{\mathbf{x}}$ and $\hat{\mathbf{y}}$.