Let

A $=$

$$

$$

$$

$$

$917$

$114$

$2110$

$714$

$$

$$

$$

$$

$,$ b$1=$

$$

$$

$$

$$

$12$

$19$

$21$

$14$

$$

$$

$$

$$

$,$ b$2=$

$$

$$

$$

$$

$33$

$10$

$72$

$56$

$$

$$

$$

$$

$(2)$

$1.$ Does a solution exist to the problem Ax $=$ b$1?$ If yes, find a solution. Is it unique?

$2.$ Does a solution exist to the problem Ax $=$ b$2?$ If yes, find a solution. Is it unique?

$3.$ Let xn in N $($A$).$ Let xs be a solution that you found. In both cases, if a solution exists, verify that

xs $+$ xn is also a solution.

$4.$ Recall that, in a tall system Ax $=$ b$,$ the least square solution is given by xls $=($ATA$)$

$1$ATb. Compute

the least square solution xls for Ax $=$ b$1$ and Ax $=$ b$2.$

$5.$ Does the least square solution of Ax $=$ b$1$ satisfy Ax $=$ b$1?$ If yes, explain why. If no$,$ explain why not.

$6.$ Does the least square solution of Ax $=$ b$2$ satisfy Ax $=$ b$2?$ If yes, explain why. If no$,$ explain why not.

Can you please do it in Matlab?