hw1 - Homework #1 1. (a) Write out the results of each step...

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Homework #1 1. (a) Write out the results of each step of Gaussian elimination on the augmented matrix form for the linear equation 2 x - 3 y + z = 1 x + y - z = 2 - 4 x + 4 z = - 1 . (b) Use back substitution to solve for x , y , and z . (c) Write out the results of each step of Gaussian elimination with row pivoting on the augmented matrix form for the same linear equation. 2. Solve the following linear system of equations using Gaussian elimination with row pivoting: 2 x 1 + x 2 + x 3 - x 4 = 4 - 4 x 1 - 2 x 2 + x 3 + 2 x 4 = - 2 2 x 1 + 2 x 2 - x 3 - 2 x 4 = - 1 - x 1 + 4 x 2 - 2 x 3 + x 4 = 0 3. (a) Solve the following linear system of equations using Gaussian elimination with row pivoting under three-digit rounding: ( 0 . 002 x - 4 y = - 2 x + 4 y = 3 (b) Solve the following linear system of equations using Gaussian elimination with row pivoting under three-digit rounding: ( 2 x - 4000 y = - 2000 x + 4 y = 3 (c) Which of the approximations is closer to the exact solution
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hw1 - Homework #1 1. (a) Write out the results of each step...

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