Consider the system A$$x $=$

$$

$$

$$

$$

$12$

$01$

$13$

$23$

$$

$$

$$

$$x $=$

$$

$$

$$

$$

$1$

$8$

$9$

$11$

$$

$$

$$

$=$ b$.$

$($a$)$ Show that this system has no solutions.

Note: Parts $($b$)$ and $($c$)$ can be done in either order depending on your method.

$($b$)$ Find the least$-$squares best approximation to a solution to A$$x $=$ b$.$

$($c$)$ Find the point in Col$($A$)$ that is closest to $$ b$.$

$($d$)$ Find the least$-$squares error of your solution