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ESPM-EEP%202010%20Lecture%2017

# ESPM-EEP%202010%20Lecture%2017 - y = A x ⇔ x = A − 1 A...

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ESPM 104/EEP 115 Fall 2010: Lecture 17 1. What does y = ax mean as a mapping of the real number line onto itself (also class notes)? 2. What does y = A x y 1 y 2 = a b c d x 1 x 2 mean as a mapping of the real plane onto itself (also class notes)? 3. The algebra of matrices: see MatrixAlgebraGetzNotes and SSG 8.4 . 4. Solution: if A 1 exists such that A 1 A = AA 1 = I , where in 2D I = 1 0 0 1 so that I x = x , then it follows that
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Unformatted text preview: y = A x ⇔ x = A − 1 A x = A − 1 y (also class notes). 5. When does A − 1 not exist? Ans: when det a b c d ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = ad − bc = (also class notes). 6. When det A ≠ then a b c d ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ − 1 = 1 ad − bc d − b − c a ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 7. Eigenvalues and Eigenvectors: see SSG 8.5 (also class notes)....
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