# I Problem understanding the SPAN

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1. May 1, 2017

### HenryFa

Hello everyone, i'm a CS student and i'm taking a course called Linear Algebra
it's very easy, but there is one thing that i'm not clearly understanding

i know how the general way to prove if given vectors span a vspace,
ex : v1,v2,v3 i put them in a Matrix form and prove the determinant Different than 0.
the logic i'm using is : k1V1 + k2V2 + K3V3 = W (W a vector in Vspace) i write it like this
(Coeff Matrix ) x (k1,k2,k3) = W
det of the coeff matrix can prove if the given vectors span

the thing is, when the coeff matrix is not Square, we cannot find the determinant
so we need to solve the augmented matrix.

in this case :
p1 = 1- x , p2 = 3 +x + 4x^2 , p3 = 5 + 2x + 7x^2 , p4 = -1+ 5x + 4x^2
i took w = (x,y,z) and to prove k1V1 + ... + k4V4 = W

to prove that these polynomials span (P2), the augmented matrix will have the last row like all zeros equal to z-x-y
what does it mean? how do i continue after that?
thanks!

2. May 1, 2017

### Staff: Mentor

This youtuber, 3blue1brown has several nice linear algebra videos and this one may help with your understanding of span: