2130_Chapter7_Notes

2130_Chapter7_Notes

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Unformatted text preview: A¡1 exists detÔAÕ 0, can be found using row reduction (also called Gaussian elimination) on the augmented matrix ÖA| I×. In linear algebra, it is learned that and A¡1 There are three elementary row operations: 1. Interchange two rows: Ri 2. Multiply a row by a nonzero scalar: αRi , α 3. Rj . 0. Add a multiple of one row to another row: Ri αRj . 14 / 17 Example If A ab , then A¡1 cd provided that det A 1 ad ¡ bc ad ¡ bc d ¡c ¡b a , 0. If A is 3 ¢ 3 or larger, use elementary row operations to reduce ÖA| I× to a matrix of the form ÖI| B×. When this process is successful, B A¡1 . Otherwise, A is singular (not invertible). We will find the inverse of the matrix A 1 3 2 ¡1 ¡1 ¡1 2 2 3 using elementary row operations. 15 / 17 8 Exa (slide 2) ¡1 ¡1 ¡1 2 1 3 2 ÖA| I× 2 1 R2 2 R3 ¡2R2 R1 R1 100 010 3001 ¡ 3 R3 2 1R 22 10 02 00 ¡1 2 ¡3 3 2 1 2 0 10 4 ¡2 1 5 ¡5 100 010 001 1 0 0 ¡3R1 R3 ¡2R1 R2 7 10 1 2 4 5 ¡ 1 ¡ 10 ¡1 2 R2 ¡1 ¡1 2 4 5 5 10 02 00 R3 ¡ 1 R3 5 100 10 01 ¡3 ¡2 3 2 0 1 ¡1 2 1 ¡4 5 1 2 ¡1 2 5...
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This note was uploaded on 03/19/2014 for the course APMA 2130 taught by Professor Bernardfulgham during the Fall '09 term at UVA.

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