Row Operations and an Augmented MatrixDate: 07/26/99 at 15:52:41 From: Shelley Tomberlin Subject: Linear systems of equations Please help! I was given this class assignment and the more I look at it, the more confused I become. These were the instructions I was given: Solve the following linear system of equations by using row operations on the augmented matrix of the system. Show ALL checks and write the final answer in ordered notation. Our professor prefers that ALL other numbers be zeroed out except the numbers in the diagonal position. a - b - d + e = -10 2a - b - 3c + d - e = 0 2b - d + e = -1 -3a + c + e = 5 a - b - 4c + d - e = 4 Thanks. Date: 07/27/99 at 05:46:18 From: Doctor Anthony Subject: Re: Linear systems of equations The augmented matrix is [ 1 -1 0 -1 1 | -10] r1 | 2 -1 -3 1 -1 | 0| r2 | 0 2 0 -1 1 | -1| r3 |-3 0 1 0 1 | 5| r4 [ 1 -1 -4 1 -1 | 4] r5 r2 = r2 + r4 + r5 [ 1 -1 0 -1 1 | -10] r1 | 0 -2 -6 2 -1 | 9| r2 | 0 2 0 -1 1 | -1] r3 |-3 0 1 0 1 | 5| r4 [ 1 -1 -4 1 -1 | 4] r5 r4 = r4 + 3.r5 [1 -1 0 -1 1 | -10] r1 |0 -2 -6 2 -1 | 9| r2 |0 2 0 -1 1 | -1] r3 |0 -3 -11 3 -2 | 17| r4 [1 -1 -4 1 -1 | 4] r5 r5 = r5 - r1 [1 -1 0 -1 1 | -10] r1 |0 -2 -6 2 -1 | 9| r2 |0 2 0 -1 1 | -1] r3 |0 -3 -11 3 -2 | 17| r4 [0 0 -4 2 -2 | 14] r5 and continuing with these row operations we end up with [1 0 0 0 0 | -3] r1 |0 1 0 0 0 | 2| r2 |0 0 1 0 0 | -1] r3 |0 0 0 1 0 | 2| r4 [0 0 0 0 1 | -3] r5 and so a = -3, b = 2, c = -1, d = 2, e = -3 - Doctor Anthony, The Math Forum http://mathforum.org/dr.math/ |
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