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 Oct 3 accepted 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? Oct 3 comment Find a $4\times 4$ matrix $A$ where $A\neq I$ and $A^2 \neq I$, but $A^3 = I$. Sure! Will certainly do. Oct 3 asked Find a $4\times 4$ matrix $A$ where $A\neq I$ and $A^2 \neq I$, but $A^3 = I$. Oct 3 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? Or would x1 and x2 alone be a preimage? Oct 3 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? Oct 3 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? Sep 12 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? Sep 12 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. Sep 12 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... Sep 12 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? Sep 12 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? Sep 12 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? Sep 12 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 $(1,-1)$ Sep 12 comment Show that the transformation T defined by $T(x_1, x_2)\; = \;…$ is NOT linear. Okay, fixed it. Sep 12 comment Show that the transformation T defined by $T(x_1, x_2)\; = \;…$ is NOT linear. Yay! Thank you. Sep 12 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) Sep 12 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? Sep 12 awarded Commentator Sep 12 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. Sep 12 asked Show that the transformation T defined by $T(x_1, x_2)\; = \;…$ is NOT linear.