Verify that the vector functions 4 e -t and x2 = are solutions to the homogeneous...

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Verify that the vector functions 4 e -t and x2 = are solutions to the homogeneous system x' = Ax = 2 -1 12 e -t x on (- 00,00), and that tet - 2 tet Xp = 12 + 8 is a particular solution to the nonhomogeneous system x' = Ax + f(t), where f(t) = 8col (e't). Find a general solution 3et to x' = Ax + f(t). (a) Verify that each of the following equations is an identity, and state the vector that is equal to both sides of the equation. x,' = Ax, x2' = Ax2= 2. 3. Verify that the vector functions 4 e -t and x2 = are solutions to the homogeneous system x' = Ax = 2 -1 12 e -t x on (- 00,00), and that tet - 2 tet Xp = 12 + 8 is a particular solution to the nonhomogeneous system x' = Ax + f(t), where f(t) = 8col (e't). Find a general solution 3et to x' = Ax + f(t). (a) Verify that each of the following equations is an identity, and state the vector that is equal to both sides of the equation. x,' = Ax, x2' = Ax2= 2. 3.