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Problem 6: Let B = {V1, V2, ..., Un} be a set of vectors in R",...

Problem 6: Let B = {V1, V2, ..., Un} be a set of vectors in R, and let T:R → R be a linear transformation such that the se

Problem 6: Let B = {V1, V2, ..., Un} be a set of vectors in R", and let T:R" → R" be a linear transformation such that the set {T(01), T(V2), ...,T(Un) } is basis for R". Show that B = {01, V2, ..., Un } is also a basis for R". Problem 7: Decide whether the following statement is true or false. If it is true, prove it. If it is false, give an example to show that it is false. Let B = {V1, V2, ..., Vn} be a basis for R", and let T : RM + Rr be a linear transformation. Then the set {T(01), T(v2),...,T(Un) } is also basis for R".
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