Verify that X(t) is a fundamental matrix for the given system and compute X(t). Then use the result that if X(t) is a fundamental matrix for the system x' = Ax, then x(t)= X(t)X¹(0)xo is the solution to the initial value problem x'=Ax, x(0) = xo- 060 x = 1 0 1 x, x(0) = 110 1 equals each side of the equation. x₁' = Ax₁ = x₂ = Ax₂ = X3' = AX3 = -3 X(t) = 060 (a) If X(t) = [x₁ (t) x₂ (t) x3 (t)] and A= 1 0 1 ⠀⠀⠀ 110 6e-t-3e-2t 8e³t e-2t 4e3t e-2t 4e³t -e-t -5e-t validate the following identities and write the column vector that

2. (a) Find the condition number of the coefficient matrix in the system X1 (1461) (²2) = (2²6) X2 as a function of d > 0. (b) Find the error magnification factor for the approximate root xa = (-1,3+6).

SOLVE THE SYSTEM USING THE MATRIX じメPOMENテAL LUSG JORDA EXPONENTIAL FORM) x(6)= 12 L7

Consider the following linear system y + The coefficient matrix is known to have eigenpairs (1, H) and (-1,): Use the method of variation of parameters to find a particular solution of this non-homogeneous system.