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Linear Algebra: how to find matrix with 4 points in plane?
I cannot figure this out. I need help:
"Four points of the plane are given with P1=(1,1), P2=(0,2), P3=(-1,0), P4=(0,-1). Construct the matrix A, whose entry in position (i,j) is the distance from Pi to Pj."
I don't understand the idea of "position" and "distance", what is an example matrix that solves this problem? Thanks!
the distance is just the length of the line segment joining two points, given by the Pythagorean theorem
for example, the distance between P1 (1,1) and P4(0,-1) is
sqrt( [change in x]^2 +[change in y]^2)
= sqrt( [1-0]^2 + [ 1- -1]^2)
= sqrt( 1 + 4) = sqrt5
thus the matrix has sqrt5 in position (1,4) ( row 1, column 4)
Of course, the distance from P4 to P1 is the same as the distance from P1 to P4, so the entry in position (4,1) is also sqrt5. (row 4, column 1)
Fill out the rest of the matrix the same way. The numbers on the main diagonal will be 0, since the distance from a point to itself is 0.
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