Talk:06-240/Homework Assignment 5

For the test, do we have to know the LaGrange formula? Although not covered in class, it is in Section 1.6, which we've been asked to read.

The test material will only be announced on Tuesday. --Drorbn 13:02, 14 October 2006 (EDT)

For question 28: "Let V be a finite-dimensional vector space over C with dimension n. Prove that if V is now regarded as a vector space over R, then dim V = 2n"... Is this a formally defined concept? (that is, while it is obvious what they mean, how could you state it rigorously)

${\mathbb {R} }$ is a subset of ${\mathbb {C} }$, so if you know how to multiply by scalars in ${\mathbb {C} }$, you automatically know how to multiply by scalar in ${\mathbb {R} }$. Thus every vector space over ${\mathbb {C} }$ is also a vector space over ${\mathbb {R} }$ (and in the same way, also over ${\mathbb {C} }$). --Drorbn 22:01, 14 October 2006 (EDT)

Hi, I think this site might help. http://mathforum.org/library/drmath/view/51973.html. Wongpak 07:06, 16 October 2006 (EDT)

Question 29a: The suggestion of beginning with $W_{1}^{}\cap W_{2}$ and extending the bases of $W_{1}$ and $W_{2}$ seems backward to me. We know the number of elements in $W_{1}$ and $W_{2}$ but we don't know the number of intersecting elements. Should we ignore this suggestion and just prove ${\mbox{dim}}(W_{1}W_{2})^{}={\mbox{dim}}(W_{1}){\mbox{dim}}(W_{2})-{\mbox{dim}}(W_{1}\cap W_{2})$?

The suggestion is not "extending the bases of" but "extending to bases of". Anyway, you are welcome to try and ignore the suggestion and prove the end result directly, except you'll find that there is no way to do that other than to follow the suggestion... --Drorbn 10:58, 16 October 2006 (EDT)