If a Symmetric Matrix is in Reduced Row Echelon Form, then Is it Diagonal?
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.
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