A=
[1 1 2 3]
[1 2 1 1]
[2 3 3 4]
find a vector b such that Ax = b has no solution. Explain why.
Let $\displaystyle b=\begin{pmatrix}b_1\\b_2\\b_3\end{pmatrix}$ , and now bring to echelon form the augmented matrix $\displaystyle \begin{pmatrix}1&1&2&3&||&b_1\\1&2&1&1&||&b_2\\2&3 &3&4&||&b_3\end{pmatrix}$ , and check for which choices of $\displaystyle b_1,\,b_2,\,b_3$ the system is incongruent (i.e.
it has no solution)
Tonio