Final answer:
To determine if vector b is a linear combination of the columns of matrix a, set up a matrix equation ax = b and solve for x. The existence of a solution indicates b is a linear combination of a's columns.
Step-by-step explanation:
The question asks whether a vector b is a linear combination of the vectors in the columns of a matrix a. To determine this, one approach is to set up a matrix equation ax = b, where a represents the matrix and x is a vector of coefficients. If there exists a solution to this equation, then b is indeed a linear combination of the columns of a. The process involves finding whether the system has a solution, which can be done through methods such as Gaussian elimination or by checking the rank of the augmented matrix (a | b).
Additionally, understanding the concept of linear equations and the integration of orthogonal projections may be useful for analyzing linear combinations and vector operations. However, additional context or specific values for the matrix a and vector b would be required to provide a definitive answer.