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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 A1.
Also, A is the inverse of B, or simply B1.
∴ 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.
 Fall '08
 Unknown

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