Determine whether b is in col A A 1 1 0 1 1 1 b 3 2Solutio

Determine whether b is in col (A) A = [1 1 0 1 - 1 1], b= [3 2]

Solution

The column space of a matrix A is the set Col(A) of all linear combinations of the columns of A.

Basically, determining whether a vector b is in Col(A) amounts to showing that the b vector is in the span of A .

In set notation, Col(A) = {b : b =Ax for some x in <R^n}.

(3 2) = 3(1 1) - 1(0 1), Hence B is in col(A).