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# Linear Transformations watch

1. Hmmm...here's another question for you :/

Which of the following are linear transformations

a. T(x y z)=(y z 0)

b. T(x y z)=(lxl -z 0)

c. T(x y z)=(x-1, x, y)

d. T(x y z)=(2x y-2 4y)
2. i think you just need to check that
if v=(x1,y1,z1) and w=(x2,y2,z2), a1,a2 E field then

T(a1v+a2w)=a1T(v)+a2T(w)=a1T(x1, y1,z1) + a2T(x2,y2,z2)

so i THINK a. is the only one. (b. since |x1| + |x2| != |x1+x2|; c. since x1-1 + x2-1 != (x1+x2) -1; d. since y1-2 + y2-2 != (y1+y2) - 2)

but i could be wrong!

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Updated: November 17, 2005
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