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2:03
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MathIsFunDaily
Theorem 1.7.4 (Symmetry of the Inverse of Invertible Symmetric Matrix)
This video introduces a proof of Theorem 1.7.4 (Symmetry of the Inverse of Invertible Symmetric Matrix). Textbook: Howard Anton, Elementary Linear Algebra, 12th edition, Wiley. Thank you for watching! For more videos, please subscribe or check out the playlist https://www.youtube.com/playlist?list=PL2mH4VHoRj6_iqFoS4j9Cn0oHoJzQuH3O
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Prove that the inverse of a symmetric nonsingular matrix is symmetric. Getting Started: To prove that the inverse of A is symmetric, you need to show that (A^-1)^T=A^-1. (i) Let A be a symmetric, nonsingular matrix. (ii) This means that A^T=A and A^-1 exists. (iii) Use the properties of the transpose to show that (A^-1)^T is equal to A^-1 | Numerade
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