Linear Algebra Example Problems - Spanning Vectors #2

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.

[TheLeo]

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[jan-willemreens]

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[michchall]

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[DhanasekaranT-dewz]

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[kabeloramodike]

Good day
I'm a bit confused - why does the augmented matrix at 1:00 have two -2 values?

[aridennis]

you lost a negative sign in there for V2.

[happyplant]

what would happen if you solve the matrix and you get infinite solutions (like if X2 was a free variable)? would it span n-space or not? thanks:)

[peaceofheart]

Then it means only linearly independent vectors can span any vector space ?