linear algebra with transformations and eigenvectors

statman101 · #1 $Old$ November 13th, 2009, 12:20 PM

please help me solve the
problem

see the attachment

step by step would help
me understand it

thanks

tonio · #2 $Old$ November 13th, 2009, 12:40 PM

Quote:

Originally Posted by statman101 $View Post$

please help me solve the
problem

see the attachment

step by step would help
me understand it

thanks

Apply T to the vectors of B and write the result as a lin. combination of the vectors in C, and then take the transpose of the coefficients matrix. For example:

$T\left(\begin{array}{c}3\\2\\3\end{array}\right)=\left(\begin{array}{c}3\\2\end{array}\right)=\underline{\underline{1}}\left(\begin{array}{c}1\\0\end{array}\right)+\underline{\underline{2}}\left(\begin{array}{c}1\\1\end{array}\right)$ $\Longrightarrow$ the first COLUMN (from the left) of the wanted matrix is $\left(\begin{array}{c}1\\2\end{array}\right.$

Now you do something simmilar with the second element of B and find the second column of the wanted matrix for T.

Tonio