MATLAB

Each week we will provide you with a list of new MATLAB commands relevant to the material on the

worksheet. You are welcome, and in fact encouraged, to use MATLAB for the calculations in Part II of the

worksheet. On Part I you must do the calculations by hand and show your work.

Here are the new commands you will likely find useful for this week's problems:

If v and w are vectors, their dot product is calculated by dot$(v,w).$

To calculate the length of the vector v $,$ use either $\sqrt[\phantom{2}]{\text{d}\text{o}\text{t}(v,v)}$ or norm$($v$).$

Part II: Concepts and connections

In this section you are required to use MATLAB to carry out any row reduction. Almost all

of the grades in this section will be awarded for your explanations of why you calculated what you did, and

what it means. When you use MATLAB, be sure to tell us that you've done so$,$ and also write down both

what commands you used and what the output was $($or include a screenshot$).$ If you do use MATLAB for

any calculations and it gives you a decimal answer, then give your final answers rounded to $2$ decimal

places.

Let vec$(v)=\left[\begin{array}{c}1\mathrm{.}5\\ -2\\ 3\mathrm{.}2\end{array}\right]$ and let vec$(w)=\left[\begin{array}{c}-1\mathrm{.}1\\ 5\mathrm{.}4\\ 2\end{array}\right].$ Find all unit vectors vec$(z)$ in $R^3$ orthogonal to both vec$(v)$ and vec$(w).$

Be sure to explain how you know that you found all possible solutions

Please do this as soon as possible