Final answer:
Expressing a column matrix b as a linear combination of the columns of matrix a involves finding scalars that, when multiplied with the columns of a, sum up to b. This requires solving a system of linear equations.
Step-by-step explanation:
To express the column matrix b as a linear combination of the columns of matrix a, we must find scalars (constants) that can be multiplied with the columns of a such that their sum equals the column matrix b. This process involves solving a system of linear equations, typically using methods such as substitution, elimination, or matrix operations like Gaussian elimination or utilizing the inverse of a matrix.
When given an example with specific matrices, we would assign variables to the unknown scalars and set up equations based on the entries of the matrices, then solve for the variables. The solutions to these variables will then give us the weights to be used for the columns of a to obtain the matrix b.