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Linear transformations on finite dimension vector spaces

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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?

3. Let U = {all[a,c; 5a,3c]},
that is U is the set of all 2 x 2 matrices A such that a(12) = 5a(11), a(22) = 3a(23)
Find a basis of U and the dimension of U.

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Solution Summary

The problems contain operations over linear transformation on finite dimension vector spaces and also finding a basis and dimension of a vector subspace.

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2. We are given the linear transformations:

T[x, y] = [1,2; 1,1][x ,y] * ...

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