Lecture Slides 10

Lecture Slides 10 - AMS 210 Applied Linear Algebra AMS 210...

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AMS 210: Applied Linear Algebra October 13, 2009 AMS 210
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Topics Today Problem Set 4 A General Solution to 2-Equation, 2-Variable Linear Systems Cramer’s Rule Examples of Cramer’s Rule Eigenvectors/Eigenvalues, Redux AMS 210
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Problem Set 4 Grades and solution on Blackboard. Maximum possible (and achieved) grade of 100. Average of 89, standard deviation of 15, and a median grade of 93. Best performance on a problem set thus far. AMS 210
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Systems Solve system of ax + by = e and cx + dy = f for x and y : x = de - bf ad - bc and y = af - ce ad - bc . Denominator identical in expressions for x and y : ad - bc . This denominator is called the determinant. Can rewrite linear system in matrix/vector algebra terms: Ax = b where A = ± a 11 a 12 a 21 a 22 ² , b = ± b 1 b 2 ² , and x = ± x 1 x 2 ² . Analogously rewrite expressions for x and y as x 1 = a 22 b 1 - a 12 b 2 a 11 a 22 - a 12 a 21 and x 2 = a 11 b 2 - a 21 b 1 a 11 a 22 - a 12 a 21 . Therefore for 2x2 matrix, determinant is det( A ) = ³ ³ ³ ³ a 11 a 12 a 21 a 22 ³ ³ ³ ³ = a 11 a 22 - a 12 a 21 . Because all n -square matrices can be viewed as forms of n -variable, n -equation linear systems, all such square matrices also have determinants. AMS 210
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This note was uploaded on 12/06/2011 for the course AMS 211 taught by Professor Shuaixue during the Fall '09 term at SUNY Stony Brook.

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Lecture Slides 10 - AMS 210 Applied Linear Algebra AMS 210...

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