Solve the following Problems from "Applied Numerical Methods with Matlab for Engineers and Scientists" by Chapra S., 3rd Edition. (Total 130 marks) Problem #1 9.2 Use the graphical method to solve 2x-6x21 =-18 -x+8x2= == 40 (15 marks) Check your results by substituting them back into the equations. Problem #2: Use Cramer's rule to solve the following equation. (15 marks) x₁+x=5 x₁-x=-1 Problem #3: Solve the following system of linear equations using Gauss Elimination method: x₁+x₂+x=6 (25 marks) x+2x+3x=14 2x+4x+x=13 Problem #5: Consider the system of linear equations given in problem 3. Calculate: a) L. and U matrices and solve for x's using LU decomposition method. (20 marks) b) Calculate the inverse of the coefficient matrix and solve for x's using matrix inversion method. (25 marks) MacBook F5 F6 00 F7 DII DD F8 F9 F10 > 67 & 7 V 8 C