Let A 3 5 2 7 7 1 6 5 2 4 6 10 and b 1 13 8 Show if possibl

Let A -3 5 2 7 7 -1 6 5 2 4 6 10 and b = -1 13 8 Show, if possible, that b is in the span of the columns of A If possible, write b as a linear combination of the columns of A.

Solution

let A=[v₁,v₂,v₃,v₄]

a) As we know:

The span of a finite, non-empty set of vectors {u1, u2, ... , un} is the set of all possible linear combinations of those vectors, i.e. the set of all vectors of the form

c1u1 + c2u2 + ... + cnun

so b is one vector of span of the columns of A

b)bis the span of the columns of A

b) b = 2v₁-v₂