Let $A=\left[\begin{array}{ccc}1& 0& -6\\ 0& 2& -3\\ -2& 8& 3\end{array}\right]$ and $b=\left[\begin{array}{c}3\\ -1\\ -13\end{array}\right].$ Denote the columns of $A$ by $a_1,a_2,a_3,$ and let $W=$Span$\{a_1,a_2,a_3\}.$

a$.$ Is $b$ in $\{a_1,a_2,a_3\}?$ How many vectors are in $\{a_1,a_2,a_3\}?$

b$.$ Is $b$ in $W?$ How many vectors are in $W?$

c$.$ Show that $a_1$ is in W$.[$Hint: Row operations are unnecessary.$]$

a$.$ Is $b$ in $\{a_1,a_2,a_3\}?$ Select the correct choice below and, if necessary, fill in the answer box$($es$)$ to complete your choice.

A$.$ No$,b$ is not in $\{a_1,a_2,a_3\}$ since it cannot be generated by a linear combination of $a_1,a_2,$ and $a_3.$

B$.$ No$,b$ is not in $\{a_1,a_2,a_3\}$ since $b$ is not equal to $a_1,a_2,$ or $a_3.$

C$.$ Yes, $b$ is in $\{a_1,a_2,a_3\}$ since, although $b$ is not equal to $a_1,a_2,$ or $a_3,$ it can be expressed as a linear combination of them. In particular, $b=(,)a_1+()a_2+()a_3.($Simplify your answers.$)$

D$.Y$ es$,b$ is in $\{a_1,a_2,a_3\}$ since $b=a$

$($Type a whole number.$)$

How many vectors are in $\{a_1,a_2,a_3\}?$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.$ There is$($are$)$ vector$($s$)$ in $\{a_1,a_2,a_3\}.$

$($Type a whole number.$)$

B$.$ There are infinitely many vectors in $\{a_1,a_2,a_3\}.$