Final answer:
The correct answer is that the equation Ax=b may not have a solution for certain b in R^n if A is a square matrix that is not invertible, hence the answer is False.
Step-by-step explanation:
The question asked whether the equation Ax=b has at least one solution for each b in the set of real numbers R^n, where A is an n x n matrix. The correct answer is B. False. The equation may not have a solution for certain b, depending on the matrix A. Specifically, for the equation Ax=b to have at least one solution for every b, the matrix A must have a non-zero determinant, implying it is invertible.
If A does not have a non-zero determinant, there may be values of b for which the equation has no solution (e.g., the system is inconsistent) or an infinite number of solutions (e.g., the system is dependent). The statement dealt with square matrices because these properties are most directly applicable to the case where the matrix is square.