Each question is correlated to the previous question, so please answer all. Thanks!

1) Derive the equations for solving system of linear equations using pivoting along the lines of the notes or the text book. 2) Apply the solution to the following case: a. 2nd order 0.1 x1 0.3x2 1 2x1 +x2 3 b. 3rd order 0.1 x1 0.3 x2 +0.4x3 1.5 x1 +3 x2 4x3 5 C. 4th order 0.1x1 +0.3 x2 + 0.4x3 + 0.5x4 = 1 x1 + x2 + x3 + x4-3 0.1 x1 3 x24x3 0.5 x47 3) Write the Matlab code (you may use existing algorithms in the notes) to solve linear systems of equation by pivoting. 4) Verify the solutions in 2 using the Matlab implementation 1) Derive the equations for solving system of linear equations using pivoting along the lines of the notes or the text book. 2) Apply the solution to the following case: a. 2nd order 0.1 x1 0.3x2 1 2x1 +x2 3 b. 3rd order 0.1 x1 0.3 x2 +0.4x3 1.5 x1 +3 x2 4x3 5 C. 4th order 0.1x1 +0.3 x2 + 0.4x3 + 0.5x4 = 1 x1 + x2 + x3 + x4-3 0.1 x1 3 x24x3 0.5 x47 3) Write the Matlab code (you may use existing algorithms in the notes) to solve linear systems of equation by pivoting. 4) Verify the solutions in 2 using the Matlab implementation