1. ## Matrix Representation

Throughout this question B = will be the basis for given by:

and S will denote the standard basis

If T : R3 R3 is the linear map which is determined by:

T(v1) = v3 , T(v2) = v2 - v1 and T(v3) = -v3 ,

write down the matrix representation [T]BB

2. Originally Posted by matty888
Throughout this question B = will be the basis for given by:

and S will denote the standard basis

If T : R3 R3 is the linear map which is determined by:

T(v1) = v3 , T(v2) = v2 - v1 and T(v3) = -v3 ,

write down the matrix representation [T]BB
Well, the most direct way would be
$Tv_1 = \left [ \begin{matrix} a & b & c \\ d & e & f \\ g & h & k \end{matrix} \right ] \left [ \begin{matrix} 1 \\ -1 \\ 0 \end{matrix} \right ] = \left [ \begin{matrix} 0 \\ 1 \\ 1 \end{matrix} \right ]$

This implies the system
$a - b = 0$
$d - e = 1$
$g - h = 1$

The other two relations give you the other six equations you need to solve for T.

-Dan

3. ## Clarification???

Hey, could someone tell me here if the answer is

4. Originally Posted by matty888
Hey, could someone tell me here if the answer is
$Tv_1 \neq v_3$

Sorry I don't have better news.

You already have the $Tv_1 = v_3$ conditions. I also get
$a + 2c = 0$
$d + 2f = 1$
$g + 2k = 2$

$b + c = 0$
$e + f = -1$
$h + k = -1$

The first row is right, though.

-Dan