Question

Find the rank of the matrix for different values of a:

Answer 1

\[\left[\begin{matrix}1 & 2 & -1 \\ -1 & 3 & 0 \\ 2 & a & 3 \end{matrix}\right]\]

\[R_2 \rightarrow R_2 + R_!\]
\[R_3 \rightarrow R_3 - 2R_1\]

\[\left[\begin{matrix}1 & 2 & -1 \\ 0 & 5 & -1 \\ 0 & a-4 & 5 \end{matrix}\right]\]

Answer 2

The answers say that r=2 for a=-1,0
and r=3 for a≠-1,0

But isn't it r=3 for every a?