- #1
Snoogx
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Homework Statement
L:R3->R3 is a dialiation by a factor of 3 of points in the plane W given by the equation z = 0 and a contraction along the line L = span({(1,0,0)}) by a factor of 3.
Find [L], but I'm mainly concerned with finding L(e31)
Homework Equations
z = 0
L(1,0,0) = (3,0,0)
L(0,1,0) = (0,3,0)
L(span(1,0,1)) = (1/3,0,1/3)
The Attempt at a Solution
L(e1) = a(1,0,0) + b(0,1,0) + c(1,0,1)
e1 = aL(1,0,0) + bL(0,1,0) + cL(1,0,1)
e1 = a(3,0,0) + b(0,3,0) + c(1/3,0,1/3)
e1 = [(3,0,0),(0,3,0),(1/3,0,1/3)][a,b,c]
[(1/3,0,0),(0,1/3,0),(-1/3,0,3)]e1 = [a,b,c]
[(1/3,0,0),(0,1/3,0),(-1/3,0,3)][1,0,0] = [a,b,c]
[a,b,c] = [1/3,0,0]
Can anyone check my work?