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Let V be a vector space and W be a subspace of V. Define the mapping n: V - V/W by jj(v)
Chapter 2, Problem 40(choose chapter or problem)
Let V be a vector space and W be a subspace of V. Define the mapping n: V - V/W by jj(v) = v + W for v V. (a) Prove that 77 is a linear transformation from V onto V/W and that N(n) = W. (b) Suppose that V is finite-dimensional. Use (a) and the dimension theorem to derive a formula relating dim(V), dim(W), and dim(V/W). (c) Read the proof of the dimension theorem. Compare the method of solving (b) with the method of deriving the same result as outlined in Exercise 35 of Section 1.6.
Questions & Answers
QUESTION:
Let V be a vector space and W be a subspace of V. Define the mapping n: V - V/W by jj(v) = v + W for v V. (a) Prove that 77 is a linear transformation from V onto V/W and that N(n) = W. (b) Suppose that V is finite-dimensional. Use (a) and the dimension theorem to derive a formula relating dim(V), dim(W), and dim(V/W). (c) Read the proof of the dimension theorem. Compare the method of solving (b) with the method of deriving the same result as outlined in Exercise 35 of Section 1.6.
ANSWER:Step 1 of 6
It is given that:
Where, 
