MAE 3210 Homework 3 Solved

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  1. Given the equations

10x1 + 2x2 x3 = 27

−3x1 − 6x2 + 2x3 = −61.5 x1 + x2 + 5x3 = −21.5,

  • Solve using naive Gauss elimination (by hand). Show all steps of the computation.
  • Substitute your results into the original equations to check your answers.2. Given the equations

x1 + 2x2 x3 = 2

5x1 + 2x2 + 2x3 = 9

−3x1 + 5x2 x3 = 1,

  • Solve by Gauss elimination with partial pivoting using code you have writtenyourself (see Figure 9.6 on page 268 of text for pseudocode – beware of typos and/or unneccessary components!).
  • Substitute your results into the original equations to check your answers.
  1. Given the equations

8x1 + 4x2 x3 = 11

−2x1 + 5x2 + x3 = 4

2x1 x2 + 6x3 = 7,

  • Solve using LU decomposition without pivoting (by hand). Show all steps ofthe computation.
  • Determine the matrix inverse using LU decomposition (by hand), and verifythat [A][A]−1 = [I].
  1. Given the equations

2x1 − 6x2 x3 = −38

−3x1 x2 + 7x3 = −34

−8x1 + x2 − 2x3 = −20,

  • Solve using LU decomposition with partial pivoting using code you havewritten yourself (see Figure 10.2 on page 286 for pseudocode – beware of typos and/or unnecessary components!).
  • Determine the matrix inverse using code you have written yourself (see Figure 10.5 on page 290 for pseudocode – beware of typos and/or unnecessary components!).
  • HW3-skuvjq.zip