Homework 7 427K - where A is the matrix-3 3-1-5 4 Find the...

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Homework 7 427K-H due Thursday March 27 Remember there is an exam on March 28 in the lecture room. 1. Find the general solution to the equation Y' = AY where A is the 3x3 matrix [ 1 0 5 ; 1 1 3 ; 0 2 1 ]. 2. If X' = AX give the eigenvalues of A and determine the stability of the fixed or equilibrium point 0 when: a) A= [ 1 , 0 , 2 ; 2 , 2 , 0 ; 5 , -2 , 3 ]. b) A = [ 1 , 0 , 1 , 4 ; 4 , -1 , 0 , 3 ; 3 , - 4 , 0 , 6 ; 1 , 0 , 0 , 10 ]. c) A = [ 1 , -3 ; -2 , 10 ] d) A = [ -2 , 1 , 0 ; -5 , -1 , 0 ; 1 , 0 , 3 ]. 3. Find the general solution of the equation y' = Ay
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Unformatted text preview: where A is the matrix [ -3 , 3 ; -1 , -5 ] 4. Find the general solution to the equation y' = Ay where A is the 3x3 matrix [ 2 , 0 , 0 ; 1 , 5 , 2 ; 3 , -2 , 5 ]. 5. Consider the 2x2 system of equations y' = Ay where the matrix A depends on an unknown parameter b. A = [ -1 , b ; -1 , 1 ]. Classify the solution [ 0 ; 0 ] as a fixed point for the various values of b. Make specific note of the value of b which is the transition point between the different behaviors of solutions to y' = Ay....
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