Chapter 3.3, Problem 38E

Let $A$ be the matrix given in Exercise 26.

a) For each vector $b$ that follows, determine whether $b$ is in $\mathcal{R}\left(A\right)$.

b) If $b$ is in $\mathcal{R}\left(A\right)$, then exhibit a vector $x$ in $R^2$ such that $Ax=b$.

c) If $b$ is in $\mathcal{R}\left(A\right)$, then write $b$ as a linear combination of the columns of $A$.

i)	$b=\left[\begin{array}{c}1\\ -3\end{array}\right]$	ii)	$b=\left[\begin{array}{c}-1\\ 2\end{array}\right]$
iii)	$b=\left[\begin{array}{c}1\\ 1\end{array}\right]$	iv)	$b=\left[\begin{array}{c}-2\\ 6\end{array}\right]$
v)	$b=\left[\begin{array}{c}3\\ -6\end{array}\right]$	vi)	$b=\left[\begin{array}{c}0\\ 0\end{array}\right]$

26. $A=\left[\begin{array}{cc}1& -2\\ -3& 6\end{array}\right]$