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The points ( x1, y1 ) , ( x2, y2), ( x3, y3) are collinear if the rank of the matrix  is
  • a)
    3
  • b)
    3 or 2
  • c)
    2 or 1
  • d)
    3 or 2 or 1
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The points ( x1,y1 ) , ( x2, y2), ( x3, y3) are collinear if the rank ...
Let A be the given matrix.Since the points are collinear, the area of the triangle formed with the following points = 0
area=/math $ x_1(y_2 - y_3) + x_2(y_3 - y_1)+ x_3(y_1 - y_2) =0$
which is nothing but det(A).
As, det(A)=0.A is singular, implying rank(A) is less than 3
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The points ( x1,y1 ) , ( x2, y2), ( x3, y3) are collinear if the rank of the matrixisa)3b)3 or 2c)2 or 1d)3 or 2 or 1Correct answer is option 'C'. Can you explain this answer?
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