Linear Algebra Solutions 67

Linear Algebra Solutions 67 - has solution xn yn x0 y0 = An...

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has solution x n y n = A n x 0 y 0 = P a b - b a n P - 1 x 0 y 0 = P r cos θ r sin θ - r sin θ r cos θ n α β = Pr n cos θ sin θ - sin θ cos θ n α β = r n [ U | V ] cos sin - sin cos ‚• α β = r n [ U | V ] α cos + β sin - α sin + β cos = r n { ( α cos + β sin ) U + ( - α sin + β cos ) V } = r n { (cos )( αU + βV ) + (sin )( βU - αV ) } . (d) The system of diFerential equations dx dt = ax + by dy dt = cx + dy is attacked using the substitution X = PY , where Y = [ x 1 , y 1 ] t . Then ˙ Y = ( P - 1 AP ) Y,
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This note was uploaded on 12/19/2011 for the course MAS 3105 taught by Professor Dreibelbis during the Fall '10 term at UNF.

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