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Math Help - determinants

  1. #1
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    determinants

    prove that (x1,y1), (x2,y2) and (x3,y3) are collinear pts iff
    determinant :
    x1 y1 1
    x2 y2 1
    x3 y3 1 is zero
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  2. #2
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    Quote Originally Posted by alexandrabel90 View Post
    prove that (x1,y1), (x2,y2) and (x3,y3) are collinear pts iff
    determinant :
    x1 y1 1
    x2 y2 1
    x3 y3 1 is zero
    If the det=0, then the matrix is singular. Since the matrix is singular, the column vectors are lin. dep.

    If a set of vectors are collinear, then the vectors are lin. dep.; hence, the det of the coefficient matrix is 0.
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