Final answer:
To determine if b is a linear combination of the vectors formed from the columns of matrix a, we check if there exists a set of scalar coefficients that can be multiplied to each column of matrix a to obtain b.
Step-by-step explanation:
In order to determine if b is a linear combination of the vectors formed from the columns of matrix a, we need to check if there exists a set of scalar coefficients that can be multiplied to each column of matrix a to obtain b.
We can represent this using the equation: b = c1a1 + c2a2 + ... + cnan, where c1, c2, ..., cn are the scalar coefficients and a1, a2, ..., an are the columns of matrix a.
To determine if this equation holds, we can use various methods such as solving a system of equations or calculating the rank of the augmented matrix [a | b]. If the rank is equal to the number of columns in a, then b is a linear combination of the vectors formed from the columns of matrix a.