No credit will be given to an answer without work. You may use other side of the sheet if you need more space. Problem 1 [10 points] solve the system using gauss-jordan elimination: x1 + 2x2 + 3x3 2x4 = 6. 3x1 + 7x2 + 8x3 4x4 = 12. Problem 2 [10 points] find the inverse of the matrix and check that your result is correct: Problem 3 [10 points] find all the real numbers such that the matrix equation (cid:20) 1 0. 2 (cid:21)(cid:20) x1 x2 (cid:21) = (cid:20) x1 x2 (cid:21) has a nonzero solutions x = [x1, x2]t . Problem 4 [10 points] give the system corresponding to the following chemical equation, nd all the solution of the system and nd the smallest solution for the chemical reaction: x1ch4 + x2o2 x3co2 + x4h2o. Problem 5 [10 points] determine whether the following matrices are equivalent by nding a reduced row echelon form.