Question 4 (Matrix exponential method) Question 4. Let A = - (3) 1 4 (i) Find eA. (ii) Find the general solution of the system below using the matrix exponential method. 3 7-(11) 7. (iii) Solve the initial value problem 4 3 y. 3 1 = 43 ) ³, y(0) = ( -2 )·

Consider the system of differential equations x = -16x1+8x2, x2 = 20x1+8x2. Rewrite this system as a matrix equation ' = Ax. =1 = help (matrices) Compute the eigenvalues of the coefficient matrix A and enter them as a comma separated list. help (numbers) Book: Section 3.4 of Notes on Diffy Qs

solve part a and b

7 Through the method of inverting the coefficient matrix, solve x+2x=8 2x - y = -5 x+y+z = 4.

X' 11 02-2 X 1 3 2 Find the general solution of the system of equation as a real value function

5. Solve the system by using the matrix exponential 0 1 *=[ ¦ ¦] -+[2] » ²»-[:] x (1) -3t -2 3 0

Express the system of differential equations in matrix notation. x' = (e ¹)x+ (at + bt³)y y' = (tan t)x+ (csct)y Write the system of equations using matrix notation. Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.) O A. OB. O C. X' y' = X y [-] 0-40

Question 4.12 Assume you have been given the following: P = [1²4 =14], 71 (4) - [2016 +46 + га -4 = [2e³ 4e¯ 15 -7. 3t 3e +10e (t) Please try and depict that derivatives and the matrix product. =4e³t + Ze 2²2²₂²² = [ -=-6e³+ + 5e-² is a valid solution to the system of -4 ==-1)ײ₂ (4) -7 ₂ (t) x = P₁² 9 x²₁₂² (t) = [₁²5 Your answers should be in terms of the variable t. enter your answers in the space provided below: is a valid collusion to the system of [] ze = Pz by assessing by assessing Now, please show that derivatives and the matrix product. 9 -4 x ²₂ (0) - [3 - 4) * 47 ) = ₂ (t)) / 15 -7 Your answers should be in terms of the variable t. enter your answers in the space provided below: =

Consider the linear system 3 *' = 27 a. Find the eigenvalues and eigenvectors for the coefficient matrix. help (numbers) help (matrices) A1 = , 01 = and help (numbers) help (matrices) 12 = , v2 = Find the real-valued solution to the initial value problem x = -3x1 – 2x2, x = 5x1+3x2, x1(0) = -4, x2(0) = 10. Use t as the independent variable in your answers. help (formulas) T2(t) help (formulas) OK Learn more Cookies help us deliver our services. By using our services, you agree to our use of cookies.

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