# Tagged: reduced row echelon form matrix

## Problem 647

Recall that a matrix $A$ is symmetric if $A^\trans = A$, where $A^\trans$ is the transpose of $A$.

Is it true that if $A$ is a symmetric matrix and in reduced row echelon form, then $A$ is diagonal? If so, prove it.

Otherwise, provide a counterexample.

## Problem 646

(a) Find all $3 \times 3$ matrices which are in reduced row echelon form and have rank 1.

(b) Find all such matrices with rank 2.