Solution Found!
Solved: Let H be an n-dimensional subspace of an
Chapter , Problem 8E(choose chapter or problem)
QUESTION:
Problem 8E
Let H be an n-dimensional subspace of an n-dimensional vector space V . Explain why H = V
Questions & Answers
QUESTION:
Problem 8E
Let H be an n-dimensional subspace of an n-dimensional vector space V . Explain why H = V
ANSWER:
Solution 8E
Step 1 of 2
Suppose that H is an n-dimensional subspace of an n-dimensional vector space V.
It means that the bases for both H and V have exactly n vectors.
The objective is to show that .
Case 1:
If , then, the dimensions of both H and V are equal to zero.
A zero-dimensional vector space is a vector space consisting only a zero element , implies .
