Using an Augmented MatrixDate: 11/21/1999 at 16:31:02 From: Katie Subject: Augmented matrices I'm really stuck on how to solve augmented matrices. I understand how you solve for 1 in cell 11 and I understand you have to add row 1 and row 2 to get a new row 2, but I don't understand what to multiply when you are adding the two equations. The problem is this: x + 3y + z = 3 x + 5y + 5z = 1 2x + 6y + 3z = 8 so the matrix becomes [1 3 1 | 3] [1 5 5 | 1] [2 6 3 | 8] So then you add row 1 [1 3 1 | 3] to row 2 [1 5 5 | 1], but what does row 1 get multiplied by? Date: 11/21/1999 at 18:30:17 From: Doctor Anthony Subject: Re: Augmented matrices [ 1 3 1 | 3 ] r1 [ 1 5 5 | 1 ] r2 [ 2 6 3 | 8 ] r3 r2 = r2-r1 [ 1 3 1 | 3 ] r1 [ 0 2 4 | -2 ] r2 [ 2 6 3 | 8 ] r3 r3 = r3-2r1 [ 1 3 1 | 3 ] r1 [ 0 2 4 | -2 ] r2 [ 0 0 1 | 2 ] r3 r2 = r2/2 [ 1 3 1 | 3 ] r1 [ 0 1 2 | -1 ] r2 [ 0 0 1 | 2 ] r3 At this stage we can see z = 2 y + 4 = -1 so y = -5 x - 15 + 2 = 3 so x = 16 The solution set is x = 16, y = -5, z = 2 - Doctor Anthony, The Math Forum http://mathforum.org/dr.math/ |
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