3. The null space of a matrix

Problem. Find a basis for the null space of

$M = \left[\begin{array}{rrrrr}1&2&1&2&3\\ 2&4&3&7&8\\ 1&2&3&8&8\end{array}\right]$.

In other words, find a basis for the vector solutions of $M$x$=$   0.

Method. This is the same as finding a basis for the solution space of the homogeneous linear equations with coefficient matrix $M$.