Let T: n"--. nm be a linear transformation. and l3 = {b J,
Chapter , Problem 102(choose chapter or problem)
Let T: n"--. nm be a linear transformation. and l3 = {b J, b2, .. . , b.,} and C = {CJ, C2, . ... c.,..} be bases for n and n'". respectively. Let B and C be the matrices whose columns arc the vectors in l3 and C. respectively. Prove the following results: (a) If A is the standard matrix ofT. then [T)~ = c-1 AB. (b) If U: n --. n'" is linear and s is any scalar. then (i) [T + U)~ = fTl~ + :
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