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Consider the four 3 × 3 linear systems having the same coefficient matrix:
2x1 − 3x2 + x3 = 2, 2x1 − 3x2 + x3 = 6,
x1 + x2 − x3 = −1, x1 + x2 − x3 = 4,
−x1 + x2 − 3x3 = 0; −x1 + x2 − 3x3 = 5;
2x1 − 3x2 + x3 = 0, 2x1 − 3x2 + x3 = −1,
x1 + x2 − x3 = 1, x1 + x2 − x3 = 0,
−x1 + x2 − 3x3 = −3; −x1 + x2 − 3x3 = 0.
a. Solve the linear systems by applying Gaussian elimination to the augmented matrix
b. Solve the linear systems by finding and multiplying by the inverse of
c. Which method requires more operations? |
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