MATH 2211 Midterm: Exam1210Sample3Ans
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Verify that if ad bc = 0, then the system of equations has a unique solution. ax1 + bx2 = r cx1 + dx2 = s. We apply row-reduction algorithm to the augmented matrix corresponding to the system given above: Assume that a = 0, then we get. 0 d c a b c r a r + s ] . a b = da bc a. By theorem 2, we know that the system above is consistent because d c a = 0 and we have da bc means that the solution is unique. Therefore, in the echelon form above, we have 2 leading entries which a. We need to examine the case a = 0. We can also solve for x1 = (s (dr/b)))/c. Finally, we conclude that the system above has a unique solution if ad bc = 0. Write the augmented matrix corresponding the system below:
