MATH 2211 Midterm: Exam1210Sample1Ans
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Determine the values of k such that the linear system is consistent. Assume that k = 0, then we get. [ 9 k k 1 3 ] ( k/9)r1+r2 r2. By theorem 2, we know that the system above is consistent if and only if there is no row of the form. [0 0 1] which implies that either we must have 1 k2. 9 = 0 or we must have 1 k2. 9 = 0 and 3 k = 0. We need to examine the case k = 0. If k = 0, then we have 9x1 = 9 or x1 = 1 and x2 = 3. Note that if k = 3 the given system is still consistent. Finally, we conclude that the system above is consistent if and only if k = 3. Determine when the augmented matrix below represents a consistent linear system.
