1. The problem statement, all variables and given/known data Determine whether the following are linear transformations from R2 into R3: 2. Relevant equations a) L(x)=(x1, x2, 1)^t b) L(x)=(x1, x2, x1+2x2)^t c) L(x)=(x1, 0, 0)^t d) L(x)=(x1, x2, x1^2+x2^2)^t 3. The attempt at a solution To show L is a linear transformation, I need to be able to show: 1. L(a*x1+b*x2)=aL(x1)+bL(x2); 2. L(x1+x2)=L(x1)+L(x2); 3. L(a*x1)=aL(x1); By looking and playing around with this, I can see how d is not a transformation, since if I let a=-1 and b=-2, then rule 3 does not hold. If I'm wrong, please correct me. But as far as a, b, and c, it looks like all three rules hold. The appendix says a is not a transformation, but I'm not sure why. It seems to me that a also satisfies the 3 conditions, what am I missing? Is there an easier way to do this? Can someone explain this to me like I'm two years old?