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Exercise 11

Avg difficulty 3.0

Show that the equation of a line in R2\mathbb{R}^{2} through (x1,y1)(x_{1},y_{1}) and (x2,y2)(x_{2},y_{2}) is given by this determinant.

det⁡((xy1x1y11x2y21))=0x1≠x2\det(\begin{pmatrix}x&y&1\\ x_{1}&y_{1}&1\\ x_{2}&y_{2}&1\end{pmatrix})=0\qquad x_{1}\neq x_{2}

Hefferon, Linear Algebra, Determinants, Exploration, Exercise 11

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Adapted from Linear Algebra © 2016 Jim Hefferon. Licensed under CC BY-SA 3.0 US. Source: Linear Algebra. Imported at revision df2262e.