Not quite. Write M for the 3x3 matrix whose columns are the vectors in R^3, i.e. (1,2,-1)' etc, and write m for the 2x3 matrix whose columns are the corresponding vectors in R^2, i.e. (1,4)' etc. Here (1,2,-1)' is the transpose of the row vector (1,2,-1) and so on..Originally Posted by Mathman24
The conditions are that T times first column of M equals first column of m, and so on, or in matrix notation T*M = m.
Then T = m*M^(-1).
Your approach would work if matrices operate on vectors by multiplication from the right. But convention has it that in this operation the matrix is on the left and the vector is on the right.
Hope this helps.