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Slides_2010_02_22

# Slides_2010_02_22 - Applied linear algebra and numerical...

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Applied linear algebra and numerical analysis Session 20 Prof. Ulrich Hetmaniuk Department of Applied Mathematics February 22, 2010

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Quizz Let A be an invertible matrix A . What is the definition of κ 2 ( A ) ? = k A k 2 A - 1 2 What is the definition of R ( A ) ? = { Ax , x R n } If A = 1 - 2 3 - 4 5 - 6 7 - 8 9 , what is the value of k A k ? = | 7 | + |- 8 | + | 9 | = 24 Let x = 123 and ˆ x = 124 . 23 What is the absolute error between x and ˆ x ? = | x - ˆ x | = 1 . 23 What is the relative error between x and ˆ x ? = | x - ˆ x | / | x | = 0 . 01 Grades: 0 (43), 1 (19), 2 (12), 3 (4), 4 (4), 5 (0)
Strategy Good strategy for AMATH 352 Attend the classes. Read the lecture notes (... and its appendices). Review the online slides (after the class). Start the homeworks early. Use the discussion board. Use office hours (UH, Course Assistants). UH: W 13:30 - 15:30 Course Assistants: M (10:30-11:30, 18:00-20:00), T (17:00-20:00), W (10:30-11:30, 17:00-20:00), Th (18:00-20:00). Understand the homework solutions.

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Review: Counting the solutions Consider a matrix A R m × n and a linear system Ax = b .
Review: Counting the solutions Consider a matrix A R m × n and a linear system Ax = b . If b / R ( A ) , then the system has no solution.

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Review: Counting the solutions Consider a matrix A R m × n and a linear system Ax = b . If b / R ( A ) , then the system has no solution. If b R ( A ) , then there is at least one solution.
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Slides_2010_02_22 - Applied linear algebra and numerical...

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