Linear algebra, determine a matrix representation A for the image of T.

[Karl Karlsson]

The plane V in R3 is given by the equation 2x + 3y + 5z = 0. The transformation
T: R3 -> R3 is given by:

Determine the matrix representation A for the image of T.

Correct answer:

What do they mean "Determine the matrix representation A for the image of T"? How do they arrive at the matrix representation that they do? My first thought was to determine the matrix by setting its columns to T (ex), T (ey), T (ez), where e is the respective column in the identity matrix but this will not be the same as the answer given above

 

[Steven G]

T is a transformation. It takes vectors from R^3 into R^3. Now there may be a Matrix A that does exactly what T does. This matrix A is the matrix representation A for the image of T.

For example suppose T: R^3 -> R^3 is given by T(x,y,z) = (z,y,x).

Can you think of a matrix A such that A(x,y,z)^t= (z,y,x)? This A is easy to find. And this A is the matrix representation A for the image of T