242LN1.3 - 1.3 Gauss-Jordan Elimination Remember though that we originally wanted to put our matrix into the ideal form 100A 0 1 0 B 0 0 1C Gaussian

242LN1.3 - 1.3 Gauss-Jordan Elimination Remember though...

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1.3. Gauss-Jordan Elimination Remember though that we originally wanted to put our matrix into the “ideal” form 1 0 0 0 1 0 0 0 1 A B C Gaussian Elimination takes us to the matrix 1 - 1 2 0 1 2 0 0 1 3 1 4 But how do we go further?
1 - 1 0 1 2 0 0 1 3 1 4
1 - 1 2 0 1 2 0 0 1 3 1 4 -------------→ 1 - 2 3 R 1 = r 1 - 2 R 3 1 - 1 0 0 1 0 0 1 - 5 1 4
1 - 1 2 0 1 2 0 0 1 3 1 4 -------------→ 1 - 2 3 R 1 = r 1 - 2 R 3 1 - 1 0 0 1 2 0 0 1 - 5 1 4 -------------→ 2 - 2 3 R 2 = r 2 - 2 R 3 1 0 0 1 0 0 0 1 - 5 - 7 4
1 - 1 2 0 1 2 0 0 1 3 1 4 -------------→ 1 - 2 3 R 1 = r 1 - 2 R 3 1 - 1 0 0 1 2 0 0 1 - 5 1 4 -------------→ 2 - 2 3 R 2 = r 2 - 2 R 3 1 - 1 0 0 1 0 0 0 1 - 5 - 7 4 ------------→ 1 + 2 R 1 = r 1 + R 2 1 0 0 0 1 0 0 0 1 - 12 - 7 4
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Question: Why would we want to do Gauss-JordanElimination?
Question: Why would we want to do Gauss-JordanElimination?
Question: Why would we want to do Gauss-JordanElimination?
3 - 3 1 1 1 5 5 8 - 4 1 8
3 3 - 3 1 1 1 5 5 8 - 4 1 8 -------------→ 1 2 SWAP ( R 1 , R 2 ) 1 1 1 3 - 3 5 5 8 1 - 4 8
3 3 - 3 1 1 1 5 5 8 - 4 1 8 -------------→ 1 2 SWAP ( R 1 , R 2 ) 1 1 1 3 3 - 3 5 5 8 1 - 4 8 -------------→ 2 - 3 1 R 2 = r 2 - 3 R 1 1 1 1 0 0 - 6 5 8 1 - 7 8
3 3 - 3 1 1 1 5 5 8 - 4 1 8 -------------→ 1 2 SWAP ( R 1 , R 2 ) 1 1 1 3 3 - 3 5 5 8 1 - 4 8 -------------→ 2 - 3 1 R 2 = r 2 - 3 R 1 1 1 1 0 0 - 6 5 5 8 1 - 7 8 -------------→ 3 - 5 1 R 3 = r 3 - 5 R 1 1 1 1 0 0 - 6 0 0 3 1 - 7 3
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The next step is to ignore the first row and firstcolumn, and work with the smaller matrix:1110-6031-73How do I change these entries into a 1 and a 0?

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