Suppose A is a 3 x3 matrix and b is a vector in R3 with the property what Ax- b has a unique solution. Explain why the columns of A must span R3 Choose the correct answer below.
a. The equation has a unique solution so for each pair of vectors x and b there is only one possible matrix A. Therefore the columns of A must span R3
b. The reduced echelon form of A must have a pivot in each row or there would be more than one possible solution for the equation Ax-b. Therefore the columns of A must span R3
c. Matrix A is a square matrix, so when computing Ax, the row-vector rule shows that the columns of A must span IR3
d. When b is written as a linear combination of the columns of A it simplifies to the vector of weights x Therefore the columns of A must span R3