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For Problems 33-34, use properties of the inverse to prove the given statement. 33. If A is an nxn invertible skew-symmetric matrix, then skew-symmetric. A-¹ is -1 34. If A is an n x n invertible symmetric matrix, then A-¹ is symmetric. 35. Let A be an n × n matrix with A¹² = 0. Prove that In - A³ is invertible with 3 (In − A³)−¹ = In + A³ + Aº + Aº. 3 6

For Problems 33-34, use properties of the inverse to prove the given statement. 33. If A is an nxn invertible skew-symmetric matrix, then skew-symmetric. A-¹ is -1 34. If A is an n x n invertible symmetric matrix, then A-¹ is symmetric. 35. Let A be an n × n matrix with A¹² = 0. Prove that In - A³ is invertible with 3 (In − A³)−¹ = In + A³ + Aº + Aº. 3 6

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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For Problems 33-34, use properties of the inverse to prove the given statement. 33. If A is an nxn invertible skew-symmetric matrix, then A-¹ is skew-symmetric. -1 34. If A is an n x n invertible symmetric matrix, then A-¹ is symmetric. 35. Let A be an n x n matrix with A¹2 = 0. Prove that In - A³ is invertible with (In − A³)−¹ = In + A³ + A6 + Aº.
Transcribed Image Text:For Problems 33-34, use properties of the inverse to prove the given statement. 33. If A is an nxn invertible skew-symmetric matrix, then A-¹ is skew-symmetric. -1 34. If A is an n x n invertible symmetric matrix, then A-¹ is symmetric. 35. Let A be an n x n matrix with A¹2 = 0. Prove that In - A³ is invertible with (In − A³)−¹ = In + A³ + A6 + Aº.
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