Problem 1. Let V be a vector space over a field F. Denote by dim(V) the...

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Problem 1. Let V be a vector space over a field F. Denote by dim(V) the dimension of V over F. (a) Let V C². Show that the vectors v₁ = = What is dime(V)? (1, 1) and v₂ = (i, 1) are a basis of V over C. (b) The vector space V scalar multiplication to RC C. Find dim(V). (c) (Bonus problem, do not turn in!) Let V be a vector space over C. Show that dim® (V) = 2 dimc (V). = C² can also be viewed as a real vector space by restriction of the Problem 1. Let V be a vector space over a field F. Denote by dim(V) the dimension of V over F. (a) Let V C². Show that the vectors v₁ = = What is dime(V)? (1, 1) and v₂ = (i, 1) are a basis of V over C. (b) The vector space V scalar multiplication to RC C. Find dim(V). (c) (Bonus problem, do not turn in!) Let V be a vector space over C. Show that dim® (V) = 2 dimc (V). = C² can also be viewed as a real vector space by restriction of the

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Solutions a Basis and Dimension of V over C To prove that v 1i and v i1 form a basis of Vwe need to ... View the full answer