If the points (x_1, y_1), (x_2, y_2) and (x_3 | vedclass

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(A) Let the matrix be $A = \begin{bmatrix} x_1 & y_1 & 1 \ x_2 & y_2 & 1 \ x_3 & y_3 & 1 \end{bmatrix}$.If the points $(x_1, y_1), (x_2, y_2)$,and $

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$3$

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(A) Let the matrix be $A = \begin{bmatrix} x_1 & y_1 & 1 \ x_2 & y_2 & 1 \ x_3 & y_3 & 1 \end{bmatrix}$.If the points $(x_1, y_1), (x_2, y_2)$,and $(x_3, y_3)$ are collinear,the area of the triangle formed by these points is zero.The area of the triangle is given by $\Delta = \frac{1}{2} |\det(A)| = 0$,which implies $\det(A) = 0$.Since the determinant of the $3 	imes 3$ matrix is zero,the rank of the matrix $A$ must be less than $3$.Furthermore,if the points are collinear,the rows are linearly dependent,and the rank is at most $2$.Specifically,the rank is $2$ if the points are not all identical,and $1$ if all points are identical.Therefore,the rank is always less than $3$.

If the points $(x_1, y_1), (x_2, y_2)$ and $(x_3, y_3)$ are collinear,then the rank of the matrix $\begin{bmatrix} x_1 & y_1 & 1 \\ x_2 & y_2 & 1 \\ x_3 & y_3 & 1 \end{bmatrix}$ will always be less than

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