Question 1: For the following system: 15 x1 + 7 x2 - 6x3 = -12 4 x1 - 5 x2 + 9 x3 = 62 11 X x2 + 4 x3 = 9 a) Use naive Gauss elimination to decompose the above system. Then, multiply the resulting [L] and [U] matrices to determine that [A] is produced. b) Use LU decomposition to solve the system. Show all the steps in the computation. c) Determine the matrix inverse. Check your results by verifying that[A][A].' = [I]