5. Use the matrices to solve the x- 2y + 3z = 4 system: 3x – 4y + z = 4 |2x +3y – 4z = –-2

Use matrices to solve x + 2y = 13x + 2y + 4z = 7−2x + y − 2z = − 1

I. Consider the following linear system: 3x1 + 9x2 + 3x3 = 6 2x1 — 2х1 — 4x2 X3 = 12 = -8 We can view this system as a matrix equation: 3 9 31 0 -1 2 12 -2 -4 Which has the form: Ax X = B To solve the original system, we can solve this equation for X by multiplying by A-1: A-1x (A x X) = A-! × B (A-1 × A) × X = A-1 × B Iz x X = A-1 × B X = A-1 x B Use the bottom equation to solve for X. Find A-1 for the matrix A and solve the original system by using A-1 and Bin the (1) equation below. X = A-1 x B (2] Use the matrix A² you just found to solve the system: 3x1 + 9x2 + 3x3 = 12 2x1 -2x1 – 4x2 X3 = 9 = -3

QUESTION 2 A vibrating spring system with damping can be mathematically described by the following second-order linear ordinary differential equation: m- dy dt2 dy dt -b +ky = F(t). Here, m represents the mass, b denotes the damping constant, & is the spring constant, and F(t) represents the applied force as a function of time. A spring constant of 13 kg/s² is fixed to a 1 kg mass with a damping constant of 4 kg/s. The system is periodically subjected to a constant force of 2 cos(t) kgm/s². Find the solution y(t), that satisfies the initial conditions y(0) = 1 and 3'(0) = 1.