Solution Found!
Let W be a subspace of a finite-dimensional vector space V, and consider the basis
Chapter 1, Problem 35(choose chapter or problem)
Let W be a subspace of a finite-dimensional vector space V, and consider the basis {ui,u2,... ,uk} for W. Let {ui,u2,... ,uk,uk+\,... ,un} be an extension of this basis to a basis for V. (a) Prove that {uk+i + W, wfc+2 4- W,... , un 4- W} is a basis for V/W. (b) Derive a formula relating dim(V), dim(W), and dim(V/W).
Questions & Answers
QUESTION:
Let W be a subspace of a finite-dimensional vector space V, and consider the basis {ui,u2,... ,uk} for W. Let {ui,u2,... ,uk,uk+\,... ,un} be an extension of this basis to a basis for V. (a) Prove that {uk+i + W, wfc+2 4- W,... , un 4- W} is a basis for V/W. (b) Derive a formula relating dim(V), dim(W), and dim(V/W).
ANSWER:Step 1 of 5
(a)
Suppose the basis of 
Since 
