Matrices

Algebra Level 4

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

\(\large{\left[ \begin{matrix} { x }_{ 1 } & { y }_{ 1 } & 1 \\ { x }_{ 2 } & { y }_{ 2 } & 1 \\ { x }_{ 3 } & { y }_{ 3 } & 1 \end{matrix} \right] } ?\)

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