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Unformatted text preview: w gives v = ( AI ) w as a desired member of the column space, as long as it is non zero. 2. You are given that: T = 1 121 ! , A = 1 245 ! , and T1 AT =31 ! . Use this information to ﬁnd a particular solution to X = AX +1 1 ! . Hint: Use the substitution X = TY to ﬁnd the Special Fundamental Matrix for the given system and then use it. Answer: We know that the Special Fundamental Matrix is given by the formula: Φ( t ) = T e3 t et ! T1 and variation of parameters gives the answer: X = Φ( t ) u where u = Φ1 ( t )1 1 ! = T e 3 t e t ! T11 1 ! We thus solve: u = Te t ! and get u = Te t ! . Thus, a particular solution is T e3 t et ! T1 Te t ! = T1 ! =1 1 ! . 2...
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 Fall '09
 EdrayGoins
 Linear Algebra, special fundamental matrix

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