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5. 0/2 points | Previous Answers ZillEngMath6 10.4.010. Solve the given initial-value problem. x'-(1 -1 X(o) 0 8 eBook Submit Answer Save Progress Practice Another Version

Answer 1

Let x' = matrix (1 1 -1 3)X + matrix (t t + 1), x(0) = matrix (0 8) A = matrix (1 1 -1 3) for eigenvalues of n mod (lambda I - A) = 0 matrix (lambda - 1 -1 1 lambda - 3) = 0 (lambda - 1)(lambda - 3) + 1 = 0 lambda^3 4 lambda + 3 + 1 = 0 lambda^2 - 4 lambda + 4 = 0 (lambda - 2)^2 = 0 lambda = 2,2 for eigenvalues lambda = 2 (lambda I - A) = 0, matrix(1 - 1 1 -1)matrix (x_1 x_2_0 = matrix (0 0) x_1 + x_2 + 0, x_1 = x_2 V_1 = matrix (-1 1) for v_2 AX(lambda I - A) V_2 = V_1 V_2 = matrix (a b) matrix 91 -1 1 -1)matrix(a b) = matrix (-1 1) a + b = -1 a = -1 - b b = 1 a = 2 V_2 = matrix (-2 1) \r\n X(t) = c