APM2613 Assignment 2 solutions 2026

APM2613 Assignment 2 solutions 2026
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, QUESTION 1

System:
4.444𝑥1 + 12850𝑥2 − 12.444𝑥3 = 12842
{ 3.333𝑥1 + 14.520𝑥2 + 8.715𝑥3 = 26.568
1.2412𝑥1 + 4.8213𝑥2 + 2.1543𝑥3 = 8.2168


1.1 (a) Gaussian Elimination (NO pivoting)

Write augmented matrix
4.444 12850 −12.444 ∣ 12842
[ 3.333 14.520 8.715 ∣ 26.568]
1.2412 4.8213 2.1543 ∣ 8.2168


Eliminate below pivot (Row 1)

Multiplier:
3.333
𝑚21 = = 0.7500
4.444
1.2412
𝑚31 = = 0.2794
4.444


Row 2:

𝑅2 = 𝑅2 − 0.75𝑅1
(3.333 − 3.333 = 0)
14.520 − (0.75)(12850) = 14.520 − 9637.5 = −9622.980
8.715 − (0.75)(−12.444) = 8.715 + 9.333 = 18.048
26.568 − (0.75)(12842) = 26.568 − 9631.5 = −9604.932


Row 3:

𝑅3 = 𝑅3 − 0.2794𝑅1
4.8213 − 3591.89 = −3587.07
2.1543 + 3.477 = 5.631
8.2168 − 3588.09 = −3579.87


Continue elimination → Back substitution

(After full reduction)

Final Answer: