[Linear Algebra] Spanning Set Theorem

We prove the spanning set theorem and do some questions on bases and finding a basis for certain subspaces.

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#LinearAlgebra #Algebra #UniversityMath #Lecture

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[countingpebbles]

If I understand your argument correctly, although v1, v2, v3 are linearly independent and they span H, since v1 and v3 are not subsets of H, {v1, v2, v3} fails to be a subset;thus, they are not a basis of H. Thanks for the video, I have enjoyed supplementing the series with my course.

[countingpebbles]

Hey, you seem to be following Lay's linear algebra quite closely, is this the text you are referring to?

[djswagmac]

@3:05 when you are are proving that when S = {v1, ..., vp} is a set and H = span{v1, ..., vp} when you take a subset of S you take a smaller sample such as {v1=[1, 2, 3], vp=[5, 7, 9]}, while H still spans {v1=[1, 2, 3], v2=[3, 7, 8], vp=[5, 7, 9]} so how does taking some subset of S still make it a basis of H? Since S is linearly independent and v2 is not a linear combo of v1 and vp, how does taking a subset of S still allow S to be a basis for H when S can't reach [3, 7, 8]

[MarekTomastik]

Hey, thanks for the video. I have a question regarding the task "Find three distinct bases for H". All three bases (B1, B2, B3) are linearly independent but since each of them contains two vectors in R3 they span just plane in R2. So they should not be bases. Is that right or am I missing something?

[ahmedossairy]

first I would thank you for your effort, but I want to tell you something
Math is a language, so I dont need too more english, I just want to see example, please solve more example in your tutorials and I think that will be helpful