Question

Describe the possible echelon forms of a nonzero 2 x 2 matrix.

Answer 1

Answer:

we approach the issue by taking note of that a 2 x 2 matrix can either have 1 0r 2 pivot columns. If the matrix has no pivot columns then every entry in the matrix must be zero.

-> if our matrix has two pivot columns then : $\left(\begin{array}{rr}-&*&0&-\end{array}\right)$

-> if our matrix has one pivot column then we have a choice to make. If the first column is pivot column then: $\left(\begin{array}{rr}-&*&0&0\end{array}\right)$

->otherwise, if the pivot column is the second column then: $\left(\begin{array}{rr}0&-&0&0\end{array}\right)$