2. Let T and S be matrix multiplication transformations from R^2 into R^3, described as
T[x, y] = [1,2; 1,1][x,y] and S[x,y] = [7,4; 6,7][x,y]
Find the transformations 2T - S, ST and TS. Do T and S commute?
2. We are given the linear transformations:
T[x, y] = [1,2; 1,1][x ,y] * ...
The problems contain operations over linear transformation on finite dimension vector spaces and also finding a basis and dimension of a vector subspace.