lecture16

lecture16 - Lecture 16 Cramer’s Rule, Eigenvalue and...

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Unformatted text preview: Lecture 16 Cramer’s Rule, Eigenvalue and Eigenvector Shang-Hua Teng Determinants and Linear System Cramer’s Rule = = ⇔ = 33 32 31 23 22 21 13 12 11 33 32 3 23 22 2 13 12 1 1 33 32 3 23 22 2 13 12 1 3 2 1 33 32 31 23 22 21 13 12 11 3 2 1 3 2 1 33 32 31 23 22 21 13 12 11 det det 1 1 a a a a a a a a a a a b a a b a a b x a a b a a b a a b x x x a a a a a a a a a b b b x x x a a a a a a a a a Cramer’s Rule • If det A is not zero, then Ax = b has the unique solution n i A a a b a a x n i i i ,..., 2 , 1 det ] , , , , , det[ 1 1 1 = = +- Cramer’s Rule for Inverse ( 29 n j i A C A ji ij ,..., 2 , 1 , det 1 = =- ( 29 A a a e a a A n i j i ij det ] , , , , , det[ 1 1 1 1 +-- = Proof: Where Does Matrices Come From? Computer Science • Graphs: G = (V,E) Internet Graph View Internet Graph on Spheres...
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This note was uploaded on 03/08/2010 for the course CS 232 taught by Professor Bera during the Spring '09 term at BU.

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lecture16 - Lecture 16 Cramer’s Rule, Eigenvalue and...

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