Lecture 4 Printed Notes

In the gauss jordan method i augment matrix a with

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Unformatted text preview: given matrix. ⎡ྎ3 5 2 6⎤ྏ A = ⎢ྎ8 7 0 7⎥ྏ ⎢ྎ ⎥ྏ ⎢ྎ1 9 4 8⎥ྏ ⎣ྏ ⎦ྏ iv) (3 × 4) ⎡ྎ3 ⎢ྎ5 Transpose of A = A T = ⎢ྎ ⎢ྎ2 ⎢ྎ ⎣ྏ6 8 1⎤ྏ 7 9⎥ྏ ⎥ྏ (4 × 3) 0 4⎥ྏ ⎥ྏ 7 8⎦ྏ Inverse of a Matrix If two square matrices are multiplied such that this product is equal to the identity matrix, then one matrix is the inverse of the other. If AB=I, where I is the identity matrix, then B is the inverse of A or simply A-1. Also, A is the inverse of B, or simply B-1. ∴ AA −1 = A −1 A = I Gauss Jordan Method for Finding the Inverse of a Matrix (Not really finished during lecture 5 but enclosed for completeness) Elementary Row Operations i) Any row of the matrix can be multiplied by a constant. ii) A multiple of one row can be added to the multiple of any other row. • Example Suppose we have the following matrix, ⎡ྎ1 0 1⎤ྏ A = ⎢ྎ5 3 1⎥ྏ , ⎢ྎ ⎥ྏ ⎢ྎ4 1 1⎥ྏ ⎣ྏ ⎦ྏ A −1 = ? In the Gaus...
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This note was uploaded on 12/14/2011 for the course ME 218 taught by Professor Unknown during the Fall '08 term at University of Texas.

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