Matrices

Algebra Level 4

\[\large \begin{bmatrix} { x }_{ 1 } & { y }_{ 1 } & 1 \\ { x }_{ 2 } & { y }_{ 2 } & 1 \\ { x }_{ 3 } & { y }_{ 3 } & 1 \end{bmatrix} \]

If the points \((x_{1},y_{1})\), \((x_{2},y_{2})\) and \((x_{3},y_{3})\) are collinear, then what is the maximum rank of the matrix above?

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