In a given basis of a vector space, a linear transformation and a given vector of this space are determinate by and (should be a column vector).
Find the matrix representation of the transformation and of the vector in a new basis such that the old one is represented by , , (they should be column vectors).
My attempt: I formed a matrix whose columns are the , , and I found its inverse. Call them and .
Then I multiplied where is the first matrix I wrote. As result, I obtained the following matrix which would be the matrix they asked for.
For the vector, I wasn't sure at all... I just multipled by and I obtained which would be the vector they ask for.
Am I right?