Talk:06-240/Homework Assignment 5 - Revision history

Drorbn: Reverted edit of 62.231.243.137, changed back to last version by Drorbn

2007-06-05T10:15:38Z

Reverted edit of 62.231.243.137, changed back to last version by Drorbn

← Older revision		Revision as of 06:15, 5 June 2007
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	Hi, I think this site might help. http://mathforum.org/library/drmath/view/51973.html. [[User:Wongpak\|Wongpak]] 07:06, 16 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</math> and <math>W_2</math> seems backward to me. We know the number of elements in <math>W_1</math> and <math>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>?		Question 29a: The suggestion of beginning with <math>W_1^{}\cap W_2</math> and extending the bases of <math>W_1</math> and <math>W_2</math> seems backward to me. We know the number of elements in <math>W_1</math> and <math>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>?

	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... --[[User:Drorbn\|Drorbn]] 10:58, 16 October 2006 (EDT)		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... --[[User:Drorbn\|Drorbn]] 10:58, 16 October 2006 (EDT)

62.231.243.137 at 05:20, 5 June 2007

2007-06-05T05:20:59Z

← Older revision		Revision as of 01:20, 5 June 2007
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	Hi, I think this site might help. http://mathforum.org/library/drmath/view/51973.html. [[User:Wongpak\|Wongpak]] 07:06, 16 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</math> and <math>W_2</math> seems backward to me. We know the number of elements in <math>W_1</math> and <math>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>?		Question 29a: The suggestion of beginning with <math>W_1^{}\cap W_2</math> and extending the bases of <math>W_1</math> and <math>W_2</math> seems backward to me. We know the number of elements in <math>W_1</math> and <math>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>?

	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... --[[User:Drorbn\|Drorbn]] 10:58, 16 October 2006 (EDT)		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... --[[User:Drorbn\|Drorbn]] 10:58, 16 October 2006 (EDT)

Drorbn: Reverted edit of 200.238.102.162, changed back to last version by Drorbn

2007-04-10T17:00:02Z

Reverted edit of 200.238.102.162, changed back to last version by Drorbn

← Older revision		Revision as of 13:00, 10 April 2007
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	Hi, I think this site might help. http://mathforum.org/library/drmath/view/51973.html. [[User:Wongpak\|Wongpak]] 07:06, 16 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</math> and <math>W_2</math> seems backward to me. We know the number of elements in <math>W_1</math> and <math>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>?		Question 29a: The suggestion of beginning with <math>W_1^{}\cap W_2</math> and extending the bases of <math>W_1</math> and <math>W_2</math> seems backward to me. We know the number of elements in <math>W_1</math> and <math>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>?

	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... --[[User:Drorbn\|Drorbn]] 10:58, 16 October 2006 (EDT)		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... --[[User:Drorbn\|Drorbn]] 10:58, 16 October 2006 (EDT)

200.238.102.162 at 16:31, 10 April 2007

2007-04-10T16:31:08Z

← Older revision		Revision as of 12:31, 10 April 2007
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	Hi, I think this site might help. http://mathforum.org/library/drmath/view/51973.html. [[User:Wongpak\|Wongpak]] 07:06, 16 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</math> and <math>W_2</math> seems backward to me. We know the number of elements in <math>W_1</math> and <math>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>?		Question 29a: The suggestion of beginning with <math>W_1^{}\cap W_2</math> and extending the bases of <math>W_1</math> and <math>W_2</math> seems backward to me. We know the number of elements in <math>W_1</math> and <math>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>?

	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... --[[User:Drorbn\|Drorbn]] 10:58, 16 October 2006 (EDT)		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... --[[User:Drorbn\|Drorbn]] 10:58, 16 October 2006 (EDT)

Drorbn at 14:58, 16 October 2006

2006-10-16T14:58:05Z

← Older revision		Revision as of 10:58, 16 October 2006
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	Hi, I think this site might help. http://mathforum.org/library/drmath/view/51973.html. [[User:Wongpak\|Wongpak]] 07:06, 16 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>?		Question 29a: The suggestion of beginning with <math>W_1^{}\cap W_2</math> and extending the bases of <math>W_1</math> and <math>W_2</math> seems backward to me. We know the number of elements in <math>W_1</math> and <math>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>?

			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... --[[User:Drorbn\|Drorbn]] 10:58, 16 October 2006 (EDT)

159.33.10.92: Q29a question

2006-10-16T12:06:42Z

Q29a question

← Older revision		Revision as of 08:06, 16 October 2006
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	Hi, I think this site might help. http://mathforum.org/library/drmath/view/51973.html. [[User:Wongpak\|Wongpak]] 07:06, 16 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>?

Wongpak at 11:06, 16 October 2006

2006-10-16T11:06:14Z

← Older revision		Revision as of 07:06, 16 October 2006
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	<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)		<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)

Drorbn at 02:01, 15 October 2006

2006-10-15T02:01:16Z

← Older revision		Revision as of 22:01, 14 October 2006
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	The test material will only be announced on Tuesday. --[[User:Drorbn\|Drorbn]] 13:02, 14 October 2006 (EDT)		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"...		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)		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)

70.24.245.27 at 23:35, 14 October 2006

2006-10-14T23:35:28Z

← Older revision		Revision as of 19:35, 14 October 2006
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	The test material will only be announced on Tuesday. --[[User:Drorbn\|Drorbn]] 13:02, 14 October 2006 (EDT)		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)

Drorbn at 17:02, 14 October 2006

2006-10-14T17:02:28Z

← Older revision		Revision as of 13:02, 14 October 2006
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	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.		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)