Matrices

Algebra Level 4

[x1y11x2y21x3y31]\large \begin{bmatrix} { x }_{ 1 } & { y }_{ 1 } & 1 \\ { x }_{ 2 } & { y }_{ 2 } & 1 \\ { x }_{ 3 } & { y }_{ 3 } & 1 \end{bmatrix}

If the points (x1,y1)(x_{1},y_{1}), (x2,y2)(x_{2},y_{2}) and (x3,y3)(x_{3},y_{3}) are collinear, then what is the maximum rank of the matrix above?

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