MATH 2211 Midterm: Exam1210Sample2Ans
Document Summary
The augmented matrix of a linear system has the form. Determine the values of a for which the linear system is consistent. We apply row-reduction algorithm to the augmented matrix corresponding to the system given above: Assume that a = 0, then we get. By theorem 2, we know that the system above is consistent if and only if there is no row of the form. Therefore, we must have either a 1 2 a = 0. We need to examine the case a = 0. If a = 0, then we have x2 = 1 and x1 = 1. Note that the case a = 2 also gives a consistent system. Finally, we conclude that the system above is consistent if and only if a = 1. Write the augmented matrix corresponding the system below: x1 6x2 4x3 = 5. Solve the system by applying the row reduction algorithm. If the system is consistent, nd the general solution set.
