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## Homework Statement

L:R

^{3}->R

^{3}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(e

^{3}

_{1})

## 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(e

_{1}) = a(1,0,0) + b(0,1,0) + c(1,0,1)

e

_{1}= aL(1,0,0) + bL(0,1,0) + cL(1,0,1)

e

_{1}= a(3,0,0) + b(0,3,0) + c(1/3,0,1/3)

e

_{1}= [(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)]e

_{1}= [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?