## 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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