Given the matrix A, do the specified operations (by hand, no Matlab): 12 12 16 1. Calculate the determinant 2. Calculate the determinant of the matrix created by replacing the last row with the first. The first row stays the same, therefore the both the first and third rows consist of 8, 7, 1. 3. Calculate the inverse of matrix A 4. Given the system of equations: 3x1 + 5x2 2x3 + 9x4 = 107 X1 + 5x2 - 4x3 - 2x, = -26 -8x, + 6x2 + 9x - 7x4 = 185 12x, - 9x2 + 10x3- 8x4 = 110 a. Express the system in matrix notation Ax = b b. Using the 3 elementary matrix operations (row interchange, scalar multiplication of row, addition of scalar multiplied row to another row), reduce the matrix to upper diagonal form. Remember to carry out all operations on both the coefficient matrix and the RHS. c. Back substitute to calculate the solution vector x. 00