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
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!)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3d4f07e6-ff0e-4dd7-9b82-622a270b91d8%2Ff11e83ec-1f1b-47e1-9e3f-23d11b6dce7f%2F4mxd3iq_processed.png&w=3840&q=75)
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!)
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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