MATM1544_lecture 30.pdf - The image part with relationship ID rId7 was not found in the file MATM1544 LECTURE 30 The inverse matrix T 27(0)51 401 9111 |

MATM1544_lecture 30.pdf - The image part with relationship...

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9/17/2015 1 The image part with relationship ID rId7 was not found in the file. T: +27(0)51 401 9111 | [email protected] | MATM1544 LECTURE 30 The inverse matrix September 17, 2015 T: 051 401 9111 [email protected] CONTENT Inverse matrix When does an inverse exist Calculation of the inverse matrix Examples Exercise
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9/17/2015 2 THE INVERSE OF A MATRIX Can we divide one matrix by another?? Then we can solve the system °± = ² by dividing on both sides by coefficient matrix °. Division with scalars (numbers): ³ ÷ ´ = ³ × 1 ´ . ´ µ¶ = · is the inverse of the number ´ . Divide by is the same as multiplying by the inverse. The number ¸ has no inverse, so division by ¸ is impossible. Also ´ × ´ µ¶ = · · = 1. Can an ¹ × ¹ matrix º have an inverse º µ¶ ? i.e. is there a matrix º µ¶ such that ºº µ¶ = » ? Obviously the zero matrix 0 does not have an inverse: 0 × ¼ = 0 ≠ » for all matrices ¼ . However, unlike numbers, there are also nonzero matrices with no inverses.
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9/17/2015 3 MULTIPLYING ON LEFT AND RIGHT WITH INVERSE. Suppose ½ × ½ matrix ° does have an inverse ° µ¾ . Then ºº µ¶ = ». (1) Is there also a matrix ¿ such that ¼º = » ?
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  • Summer '20
  • Matrices, #, Invertible matrix, 0 0 1 Gauss

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