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why not? Let A = -2 0 1 and b = 0 21 4 Is b in the column space of A? Why or

why not? Let A = -2 0 1 and b = 0 21 4 Is b in the column space of A? Why or

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Theorem 2 1. If A is invertible, then A-¹ is invertible and (A-¹)-¹ = 2. If A and B are n x n invertible matrices, then so is AB and (AB)-¹ = = 3. If A is invertible, then so is AT and (AT)-¹ = (A-¹)¹. Question: How do we find A-¹ if A is an n x n matrix where n > 2? Answer: Algorithm: Row reduce the augmented matrix [AI]. If A is row equivalent to I, then [AI] is row equivalent to [IA-¹]. Otherwise A doesn't have an inverse. Example: A = (17). find A¹ using the algorithm. (Why did I choose a 2 x 2? Process is the same and in all reality computing A-¹ is EXPENSIVE!)
Transcribed Image Text:Theorem 2 1. If A is invertible, then A-¹ is invertible and (A-¹)-¹ = 2. If A and B are n x n invertible matrices, then so is AB and (AB)-¹ = = 3. If A is invertible, then so is AT and (AT)-¹ = (A-¹)¹. Question: How do we find A-¹ if A is an n x n matrix where n > 2? Answer: Algorithm: Row reduce the augmented matrix [AI]. If A is row equivalent to I, then [AI] is row equivalent to [IA-¹]. Otherwise A doesn't have an inverse. Example: A = (17). find A¹ using the algorithm. (Why did I choose a 2 x 2? Process is the same and in all reality computing A-¹ is EXPENSIVE!)
why not? Let A = -1 -2 0 0 1 2 1 and b -4 Is b in the column space of A? Why or
Transcribed Image Text:why not? Let A = -1 -2 0 0 1 2 1 and b -4 Is b in the column space of A? Why or
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