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 Oct3 comment What do I do if I've been asked to find the preimage of a vector, but the inverse of the Transformation Matrix doesn't exist? I found x1 and x2. Are you saying I now need to find them under T? Oct3 asked What do I do if I've been asked to find the preimage of a vector, but the inverse of the Transformation Matrix doesn't exist? Sep12 comment A linear transformation $T$ is defined by $T(x_1, x_2)$ Find the image of the line that passes through the origin and point $(1,-1)$ Ok, would you say that Hagen is correct? Sep12 comment A linear transformation $T$ is defined by $T(x_1, x_2)$ Find the image of the line that passes through the origin and point $(1,-1)$ Rather, I don't see why you combine $x_1$ and $x_2$ into t. Sep12 comment A linear transformation $T$ is defined by $T(x_1, x_2)$ Find the image of the line that passes through the origin and point $(1,-1)$ I think my study guide is looking for a more specific answer... Sep12 comment A linear transformation $T$ is defined by $T(x_1, x_2)$ Find the image of the line that passes through the origin and point $(1,-1)$ What about the use of a matrix? How would I set this up? Sep12 comment A linear transformation $T$ is defined by $T(x_1, x_2)$ Find the image of the line that passes through the origin and point $(1,-1)$ What about the use of matrices? Sep12 comment A linear transformation $T$ is defined by $T(x_1, x_2)$ Find the image of the line that passes through the origin and point $(1,-1)$ Where did you get -3t, 3t, and 3t from? Sep12 asked A linear transformation $T$ is defined by $T(x_1, x_2)$ Find the image of the line that passes through the origin and point $(1,-1)$ Sep12 comment Show that the transformation T defined by $T(x_1, x_2)\; = \;…$ is NOT linear. Okay, fixed it. Sep12 comment Show that the transformation T defined by $T(x_1, x_2)\; = \;…$ is NOT linear. Yay! Thank you. Sep12 comment Show that the transformation T defined by $T(x_1, x_2)\; = \;…$ is NOT linear. Would this proof also be correct? T(4+1, 2+2) = T(5, 4) = (17, 25); and T((4, 2)) + T((1, 2)) = (12, 14) + (-3, 8) = (9, 22); proof: (17, 25) != (9, 22) Sep12 comment Show that the transformation T defined by $T(x_1, x_2)\; = \;…$ is NOT linear. Okay, I did... T(4+1, 2+2) = T(5, 4) = (17, 25); and T((4, 2)) + T((1, 2)) = (12, 14) + (-3, 8) = (9, 22); proof: (17, 25) != (9, 22)... correct? Sep12 awarded Commentator Sep12 comment Show that the transformation T defined by $T(x_1, x_2)\; = \;…$ is NOT linear. I think T(4, 2) would actually be (12, 14), but your point still holds. Sep12 asked Show that the transformation T defined by $T(x_1, x_2)\; = \;…$ is NOT linear. Sep12 comment How do I determine linear independence when I don't know the values of the vectors? Oh I see now. That makes much more sense, thank you! Sep12 comment How do I determine linear independence when I don't know the values of the vectors? @EuYu I feel like I'm missing the obvious. I don't see how to prove that they are NOT linear combinations. As far as finding a combination goes, I don't know how to prove dependence with just variables. You've pretty much narrowed it down for me, but I still don't get it. Sep11 comment How do I determine linear independence when I don't know the values of the vectors? @EuYu, The coefficients of v2 and v3 are linear combinations of one another. Thus, the family is not independent? Sep11 comment How do I determine linear independence when I don't know the values of the vectors? I think you are making typos that confused me, sorry for the confusion.