Use the variation of parameters formula to find a general solution of the system x'(t) = Ax(t) + f(t), where A and f(t) are given. A = - 16 4 4 -1 f(t)= 7+4t_1 ( Let x(t) = x₁(t) + xp (t), where x₁ (t) is the general solution corresponding to the homogeneous system, and xp (t) is a particular solution to the nonhomogeneous system. Find x₁ (t) and x (t).

Solve the given linear system by any method. (2x - y - 3z = 0), (x + 2y - 3z = 0), (x + y + 4z = 0). **I used Row-Echelon form and got the answer "The homogeneous linear system has a trivial solution of x = y = z = 0." Is this correct?

Use EROS and backward substitution to solve the system Ax= b, where (三) (6) 21 1 and 1. -3 -1 What is the rank of A?

Write the given system in the form x' = P(t)x+ f(t). x' = 3x-7y+z+t y' = x-5z+t²2² z' = 3y - 5z+t³ ---