Talk:06-240/Homework Assignment 5

2006-10-16T12:06:42Z

159.33.10.92: Q29a question

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. --[[User:Drorbn|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)

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

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

Question 29a: The suggestion of beginning with <math>W_1^{}\cap W_2</math> and extending the bases of <math>W_1^{}\mbox{ and }W_2</math> seems backward to me. We know the number of elements in <math>W_1^{}\mbox{ and }W_2</math> but we don't know the number of intersecting elements. Should we ignore this suggestion and just prove <math>\mbox{dim}(W_1+W_2)^{}=\mbox{dim}(W_1)+\mbox{dim}(W_2)-\mbox{dim}(W_1\cap W_2)</math>?

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Talk:06-240/Homework Assignment 5