For this exercise assume that the matrices are all nxn. The statement in this exercise is an implication of the form "If "statement 1", then "statement 2"." Mark an implication as True if the truth of "statement 2" always follows whenever "statement 1" happens to be true. Mark the implication as False if "statement 2" is false but "statement 1" is true. Justify your answer. If the equation Ax=b has at least one solution for each b in R", then the solution is unique for each b. Choose the correct answer below. O A. The statement is true. By the Invertible Matrix Theorem, if Ax=b has at least one solution for each b in R", then matrix A is invertible. If A is invertible, then according to the invertible matrix theorem the solution is unique for each b. OB. The statement is true, but only for x +0. By the Invertible Matrix Theorem, if Ax=b has at least one solution for each b in R", then the equation Ax=0 does not only have the trivial solution. OC. The statement is false. By the Invertible Matrix Theorem, if Ax=b has at least one solution for each b in R", then the linear transformation x → Ax does not map R onto R. O D. The statement is false. By the Invertible Matrix Theorem, if Ax=b has at least one solution for each b in R", then matrix A is not invertible. If A is not invertible, then according to the Invertible Matrix Theorem, the solution is not unique for each b.

Which of the following statements are true? Remember that a mathematical statement is said to be true if it is always true, under all circumstances. VA. The solution set of a linear system whose augmented matrix is aj az az | 6 is the same as the solution set of Ах — b, if A — [ај ар аз |- V B. A vector b is a linear combination of the columns of a matrix A if and only if the equation Ax = b has at least one solution. VC. If A is an m × n matrix and if the equation Ax = b is inconsistent for some b in R", then A cannot have a pivot in every row. D. The equation Ax = b is referred to as a vector equation. VE. If the augmented matrix A | b] has a pivot position in every row, then the equation Ax = b is inconsistent. O F. The first entry in the product Ax is a sum of products.

WHe-the sytems of equations as an augmented "matrix X-34-32= - -5X-3+57=-a (-bX-5y42=-le

Use Cramer’s Rule to solve the systemx + 3y - z = 1-2x - 6y + z = -33x + 5y - 2z = 4