Please help me to answer the question below in detail. I really don't understand it. This's all the information I got for the question.Thank you so much, and have a great day!

5. Let 8 = {el, e2, e3} be the standard basis for R3. (a) Give a basis * for R that is not the standard basis. (b) Define a linear transformation T that maps 8 to *, i.e. T(B) = *. Can you find a matrix A so that T(v) = A . v? (c) Generalize the process in part (b) for any basis , so that you can construct a matrix that maps the standard basis to 81. (d) Is the matrix in part (c) invertible? Explain. (e) What sources did you use for this exercise