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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.