# Math Help - find a vector b such that Ax = b has no solution

1. ## find a vector b such that Ax = b has no solution

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.

2. Originally Posted by dusty
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 $b=\begin{pmatrix}b_1\\b_2\\b_3\end{pmatrix}$ , and now bring to echelon form the augmented matrix $\begin{pmatrix}1&1&2&3&||&b_1\\1&2&1&1&||&b_2\\2&3 &3&4&||&b_3\end{pmatrix}$ , and check for which choices of $b_1,\,b_2,\,b_3$ the system is incongruent (i.e.

it has no solution)

Tonio