Find the Rank of a Matrix with a Parameter
Problem 103
Find the rank of the following real matrix.
\[ \begin{bmatrix}
a & 1 & 2 \\
1 &1 &1 \\
-1 & 1 & 1-a
\end{bmatrix},\]
where $a$ is a real number.
(Kyoto University, Linear Algebra Exam)
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