$14.$ Run the commands:

zeros$53=$zeros$(5,3)$;

ones$42=$ones$(4,2)$;

Variables: zeros$53,$ ones$42$

Q$6$: What do the functions zeros and ones do$?$

$15.$ Generate the diagonal $3\backslash$times $3$ matrix S with the diagonal elements $\{1,3,7\}$ using the

Matlab diag function. To learn about diag type help diag in the command line.

Variables: S

$16.$ Now we want to extract the diagonal elements of a matrix and save them in a separate

vector. The same function diag accomplishes that as well. Type

R$=$rand$(5,5)$

diagR$=$diag$($R$)$

This creates a matrix R with random entries from the interval $(0,1),$ extracts the

diagonal entries from it$,$ and saves them in the vector diagR. Observe that the function

diag has other interesting possibilities $($use help diag$).$

Variables: R$,$diagR

$17.$ Alternatively we can use spdiags. This creates a sparse matrix $($with a large number

of zeros$),$ so that Matlab only stores the non$-$zero entries. To convert sparse form to

dense form, use the command full. Run the following code:

diag$121=$spdiags$([-$ones$(10,1)2*$ones$(10,1)-$ones$(10,1)],[-101],10,10)$;

full$($diag$121)$

Variables: diag$121$

Q$7$: What does this code do$?$

$6$