Answer:
Explanation:
heyy!!
this is true. if for some matrix A and some vectors x, b, we have AX = b, then b is in the span of the column vectors of A.
to understand why this is true, let's break it down:
1. The product of a matrix A and a vector x, AX, is a linear combination of the column vectors of A, where the coefficients of the linear combination are the elements of x.
2. If AX = b, it means that b can be expressed as a linear combination of the column vectors of A, with the coefficients given by the elements of x.
3. Therefore, b lies in the span of the column vectors of A, since it can be represented as a combination of those vectors
basically, if AX = b, then b is in the span of the column vectors of A.
hope that helped!! :)