Suppose the coefficient matrix of a linear system of four equations in four variables has a pivot in each column. Explain why the system has a unique solution.

the matrix described in the question is a linearly independent matrix, and linearly dependent matrix has a unique solution. see further explanation below

Step-by-step explanation:

For any matrix to have a pivot column in all its column, it means that the matrix must be linearly dependent

Thus, as the columns are linearly independent, the system of equation have a unique solutions.