determinants

• Nov 23rd 2009, 01:27 PM
alexandrabel90
determinants
how do you prove that (x1, y1), (x2,y2), (x3,y3) are collinear pts iff det of
lx1,y1,1l
lx2,y2,1l
lx3,y3,1l is 0.

the above is a 3x3 matrix.
• Nov 23rd 2009, 07:44 PM
tonio
Quote:

Originally Posted by alexandrabel90
how do you prove that (x1, y1), (x2,y2), (x3,y3) are collinear pts iff det of
lx1,y1,1l
lx2,y2,1l
lx3,y3,1l is 0.

the above is a 3x3 matrix.

.
• Nov 23rd 2009, 11:35 PM
alexandrabel90
sorry, i cant seem to see what you have typed:/
• Nov 24th 2009, 12:27 AM
Shanks
The area of the triangle formed by the three given point is half of the absolute value of determinant.
Thus if the three points are colinear, then the determinant is equal to 0.
• Nov 24th 2009, 01:41 AM
alexandrabel90
what does it mean that the area formed by the 3 given pts is half the absolute value of the determinant?

could you explain further?
thank you!
• Nov 24th 2009, 02:21 AM
Shanks
This is the formulla to find the area of a triangle formed by three points whose coordinates are given.