1
Question
The value of x3 obtained by solving the following system of linear equations is
x1+2x2−2x3=4
2x1+x2+x3=−2
−x1+x2−x3=2
The value of x3 obtained by solving the following system of linear equations is
x1+2x2−2x3=4
2x1+x2+x3=−2
−x1+x2−x3=2
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Solution
The correct option is B - 2
[A:B]=⎡⎢
⎢
⎢
⎢⎣12−2⋮4211⋮−2−11−1⋮2⎤⎥
⎥
⎥
⎥⎦
R2→R2−2R1
R3→R3+R1
[A:B]=⎡⎢
⎢
⎢
⎢⎣12−2⋮40−35⋮−10002⋮−4⎤⎥
⎥
⎥
⎥⎦
So, Ax = B [A:B]=⎡⎢⎣12−20−35002⎤⎥⎦⎡⎢⎣x1x2x3⎤⎥⎦=⎡⎢⎣4−10−4⎤⎥⎦
⇒x1+2x2−2x3=4
−3x2+5x3=−10
2x3=−4
Hence, x3=−2
[A:B]=⎡⎢ ⎢ ⎢ ⎢⎣12−2⋮4211⋮−2−11−1⋮2⎤⎥ ⎥ ⎥ ⎥⎦
R2→R2−2R1
R3→R3+R1
[A:B]=⎡⎢ ⎢ ⎢ ⎢⎣12−2⋮40−35⋮−10002⋮−4⎤⎥ ⎥ ⎥ ⎥⎦
So, Ax = B [A:B]=⎡⎢⎣12−20−35002⎤⎥⎦⎡⎢⎣x1x2x3⎤⎥⎦=⎡⎢⎣4−10−4⎤⎥⎦
⇒x1+2x2−2x3=4
−3x2+5x3=−10
2x3=−4
Hence, x3=−2
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