Solve the following system of equations 5x_1 – 6x_2 + x_3 = -4 – 2x_1 + 7x_2 + 3x_3 = 21 3x_1 -12x_2 -2x_3 = -27 with :
a) naive Gauss elimination, b) Gauss elimination with partial pivoting, c) Gauss-Jordan without partial pivoting, d) LU decomposition without pivoting. e) Determine the coefficient matrix inverse using LU decomposition in (d). Check your results by verifying that [A][A]^-1 = [I]
