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Fundamental theorem of linear algebra revisited - take a look at the challenge problem

C)

$${\vec{x}}_{w^{\perp }}=\vec{x}-{\vec{x}}_w$$ $${\vec{x}}_{w}inCol(a)$$ $${\vec{x}}_{w^{\perp }}inNul(A^{transpose})$$

d)

WW. 14.6.3

$$\vec{v}=(8,10,-7,0)$$

Find the closest point to v in the subspace W.

$$letW=span\{(6,4,6,1),(6,3-4,-24)\}$$

Declare a matrix that is composed of the two vectors in the span of W. It transforms R2 to R4, so W = Col(A) ?

$${\vec{v}}_w=A\vec{c}=A(A^{T}A{)}^{-1}{A}^T\vec{v}$$