Final answer:
The question is concerned with whether a vector b is in the set w, which consists of all linear combinations of the columns of a matrix a. The approach involves setting up an augmented matrix and performing row operations. Without specific matrix entries, a numerical example cannot be provided.
Step-by-step explanation:
The question is asking whether a vector b can be expressed as a linear combination of columns of a matrix a. In essence, we need to determine if there are coefficients that can be applied to the columns of a such that their linear combination adds up to b. This is essentially asking if b is in the span of the columns of a, also known as the column space of a, which we denote as w.
Since the exact column entries of a and b are not clearly specified, the general approach to solving this problem would be to set up an augmented matrix with a on the left and b on the right. Then perform row operations to reduce the matrix to row echelon form or reduced row echelon form. If a solution exists (meaning b is a linear combination of the columns of a), then b will be in w. Otherwise, b is not in w.
To demonstrate this procedure, consider matrices with well-defined entries and perform matrix operations to find the result. However, as the question does not provide clear matrices to work with, it is not possible to provide a specific numerical example.