Linear AlgebraChallengeRow Reduction & Rank

Row Reduction & Rank · Challenge problem

Gaussian elimination without row exchanges is applied to

A = \begin{pmatrix} 1 & a & 0 \\ a & 1 & a \\ 0 & a & 1 \end{pmatrix}, \qquad 0 < a < 1.

For which value of $a$ is the third pivot equal to $0$ ?