Use the matrix inverse method to solve the following system of equations. So first, find the inverse of the coefficient matrix and then use this inverse to find the value of x₁ and x₂ and x₃. (There are no fractions in this problem.)

x₁ + x₂ + 2x₃ = 3

2x₁ + 3x₂ + 2x₃ = 4

x₁ + x₂ + 3x₃ = 5

Note to receive credit you must include the following:

1. Work showing the calculation of the inverse, A^-1
2. Clear identification of the inverse matrix A^-1.
3. Work showing how you use A^-1 to find the values of x₁ and x₂ and x₃
4. State your solution clearly at the end of the problem