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What are basis vectors in a transofrm?

Updated: 9/22/2023
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Q: What are basis vectors in a transofrm?
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How do you find the dimension of the subspace of R4 consisting of the vectors a plus 2b plus c b-2c 2a plus 2b plus c 3a plus 5b plus c?

The dimension of a space is defined as the number of vectors in its basis. Assuming your vectors are 1,2,1,0 0,1,-2,0 2,2,1,0 and 3,5,1,0 (extra zeros because you are in R4) then you must first check to see if they are linearly indepent. If all the vectors are linearly independent then the subspace defined by those vectors has a dimension 4, as there are 4 vectors in the basis.


Can any vector be represented by two other vectors that are right angels to each others?

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If a set of vectors spans R3 then the set is linearly independent?

No it is not. It's possible to have to have a set of vectors that are linearly dependent but still Span R^3. Same holds true for reverse. Linear Independence does not guarantee Span R^3. IF both conditions are met then that set of vectors is called the Basis for R^3. So, for a set of vectors, S, to be a Basis it must be:(1) Linearly Independent(2) Span S = R^3.This means that both conditions are independent.


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A plane has no vertices, so you can't. Pick one or three spicks (points) in the plane, usually at the basis vectors, for its label.


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Two vectors: no. Three vectors: yes.


What has the author Jarvis written?

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Vectors that sum to zero are coplanar and coplanar vectors sum to zero.