STEM Lessons for College Students

Linear Algebra Example Problems – Spanning Vectors #2

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In this problem we work with the vectors v1 and v2 and determine if the set {v1, v2} spans R2.

If the set of vectors {v1,v2} spans R2, then ANY vector from R2 can be written as a linear combination of these vectors. To see if this is true, an arbitrary vector from R2 is selected an and an augmented matrix is constructed and solved. If there is no solution to this system of equations, then the set of vectors {v1,v2} does not span R2.

Obviously, this approach can be extended to spaces with higher dimension.

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