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. D. The system has at least one free variable.
E. The system is consistent.
F. The system has no free variables.
Use the given assumption that the coefficient matrix of the linear system of four equations in four variables has a pivot in each column to determine the dimensions of the coefficient matrix. The coefficient matrix has four rows and four columns. Let the coefficient matrix be in reduced echelon form with a pivot in each column, since each matrix is equivalent to one and only one reduced echelon matrix. Construct a matrix with the dimensions determined in the previous slop that is in reduced echelon form and has a pivot in each column.