1) Solve the following system of equations 5x1​−6x2​+x3​=−4−2x1​+7x2​+3x3​=213x1​−12x2​−2x3​=−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].