-3 -12 -24 Let A = -8 -13 -32 6 12 27 The eigenvalues of A...

 
 

Transcribed Image Text:

-3 -12 -24 Let A = -8 -13 -32 6 12 27 The eigenvalues of A are 5 and 3. The matrix A is diagonalizable with A = PDP-1 By using the diagonalization above, find the solution to -3f1 -8f1 6f1 Define functions 81,82,83 by fi $₂ = f3 = fi(x) = f2(x) = f3(x) = 12f₂ 13f₂ +12f2 - where f1, f2 and f3 are differentiable functions, subject to the constraints f(0) = -3 ƒ₂ (0) = 2 ƒ3 (0) = 9. 81 E- 83 24f3 32f3 +27f3 fi f2 f3 - Using the P and D that you obtained above and using C₁, C2, C3 as the constants appearing in the functions 81, 82, 83, respectively, the general solution to this system is Note: this part is graded as incorrect if your work above is incorrect. (Hint: to enter an answer of the form c₁e4x c₂e-8x type c_1e^(4x) - c_2e^(-8x).) Using the given constraints we obtain f₁(x) = f₂(x) = f3(x) = (Hint: to enter an answer of the form 3e4x type 3*e^(4x).) -3 -12 -24 Let A = -8 -13 -32 6 12 27 The eigenvalues of A are 5 and 3. The matrix A is diagonalizable with A = PDP-1 By using the diagonalization above, find the solution to -3f1 -8f1 6f1 Define functions 81,82,83 by fi $₂ = f3 = fi(x) = f2(x) = f3(x) = 12f₂ 13f₂ +12f2 - where f1, f2 and f3 are differentiable functions, subject to the constraints f(0) = -3 ƒ₂ (0) = 2 ƒ3 (0) = 9. 81 E- 83 24f3 32f3 +27f3 fi f2 f3 - Using the P and D that you obtained above and using C₁, C2, C3 as the constants appearing in the functions 81, 82, 83, respectively, the general solution to this system is Note: this part is graded as incorrect if your work above is incorrect. (Hint: to enter an answer of the form c₁e4x c₂e-8x type c_1e^(4x) - c_2e^(-8x).) Using the given constraints we obtain f₁(x) = f₂(x) = f3(x) = (Hint: to enter an answer of the form 3e4x type 3*e^(4x).)