1.Solve the following equations by the
Gauss elimination method
► 2x - y + 3z = 9;
X + y + z = 6;
X-y + z = 2;
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a) x = 1.64791, y = 1.14085, z = 2.08451
b) x = 1.65791, y = 1.14185, z = 2.08441
c) x = 1.64691, y = 1.14095, z = 2.08461
d) x = 1.64491, y = 1.15085, z = 2.09451
Answer: a
Explanation: By Gauss Elimination method we get
⎡⎣⎢11341−1−1−6−1⎤⎦⎥ ⎡⎣⎢xyz⎤⎦⎥ = ⎡⎣⎢−5−124⎤⎦⎥
By R2-R1 and R3-3R1
⎡⎣⎢1004−3−13−1−52⎤⎦⎥ ⎡⎣⎢xyz⎤⎦⎥ = ⎡⎣⎢−5−719⎤⎦⎥
R3-(-13/-3)*R2
⎡⎣⎢1.0000004.0000−3.00000−1.0000−5.000023.6667⎤⎦⎥ ⎡⎣⎢xyz⎤⎦⎥ = ⎡⎣⎢−5−749.33333⎤⎦⎥
x+4y-z = -5
-3y-5z = -7
23.6667z = 49.3333
Hence, z = 2.08451
-3y = -7+5z
Hence, y = -1.14085
x = -4y+z-5
Hence, x = 1.64791.
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