Question

what is matrix of linear transformation? how to write it?

Answer 1

this is one of the best site for info:
http://tutorial.math.lamar.edu/Classes/LinAlg/LinearTransformations.aspx

Answer 2

can I write linear transformation here and you write me matrix? :)

Answer 3

this one too:
http://en.wikipedia.org/wiki/Transformation_matrix

If one has a linear transformation T(x) in functional form, it is easy to determine the transformation matrix A by simply transforming each of the vectors of the standard basis by T and then inserting the results into the columns of a matrix. In other words,
A= [ T(e1) T(e2).... T(e n) ]

it's hard to write matrices here - please see links

Answer 4

it won't be hard, it's 3x3 matrix, just write which matrix did u get. I did something, but I'm not sure if it's correct.
I got matrix [ 1, -6, 5; 2, 9 -5; 0, 0, 0]. Is this good?

Answer 5

sorry... just got back
here we go:

Answer 6

Example: The columns of
\[I1=\left[\begin{matrix}1 & 0 \\ 0 & 1\end{matrix}\right]\]
are
\[e1=\left(\begin{matrix}1 \\ 0\end{matrix}\right) and e2=\left(\begin{matrix}0 \\ 1\end{matrix}\right)\]
Suppose T is a linear transformation from R2 to R3 such that

Answer 7

\[T(e1)=\left(\begin{matrix}5 \\ -7\\ 2\end{matrix}\right)\]
and
\[T(e2)=\left(\begin{matrix}-3 \\ 8\\ 0\end{matrix}\right)\]

To find a formula for the image of an arbitrary x in R2 write:
\[x=\left(\begin{matrix}x1 \\ x2\end{matrix}\right)=x1\left(\begin{matrix}1 \\ 0\end{matrix}\right)+x2\left(\begin{matrix}0 \\ 1\end{matrix}\right)\]

Answer 8

=x1e1 +x2e2

Since T is a linear transformation,
T(x)=x1*T(e1) +x2*T(e2)=
......=
\[\left(\begin{matrix}5x1-3x2 \\ 7x1+8x2\\ 2x1+0\end{matrix}\right)\]
You can re-write it as:
T(x)=[T(e1) T(e2) [x1/x2] = Ax