Using Matlab, normalize the input vectors, check that they are orthogonal,

and construct an associative matrix that maps the following vector pairs:

Use the matrix from #$1,$ and multiply it by the average of the normalized s$1$ and s$2.$

Explain the result.

Generate $3$ random vectors $s1,s2,s3$ of $100$ dimensions and normalize them.

Calculate the $3$ by $3$ cosine matrix. Associate the new s$1,$ s$2,$ s$3$ with T$1,$ T$2,$ and T$3$

from exercise $1.$ Construct an associative matrix and compare the responses R$1,$ R$2,$ R$3$

to the target vectors. Repeat for $10000$ dimensions.

Create a surface plot of a cylinder $($like the one below$)$ in Matlab. Show your Matlab

commands.

$[$HINT: There are two circles $,$ and $y=sin(a).$ One circle is at $z=0,$ and one is

above it$,$ at $z=1]$