Let x1u1+x2u2+x3u3=vx∈R
⎣⎡1−322−4−11−37⎦⎤⎣⎡x1x2x3⎦⎤=⎣⎡2−53⎦⎤
Considering augmented matrix A for this system and applying Gauss- Jordan elimination
A=∣∣∣1−322−4−11−37∣∣2−53∣∣
−31 R2−R1→R2
∣∣∣1012−32−211027∣∣2−3123∣∣
21R3−R1→R2
∣∣∣1002−32−251025∣∣2−31−21∣∣
−23R2→R2 ∣∣∣10021−251025∣∣221−21∣∣
−52R3−R2→R3
∣∣∣10021010−1∣∣221−103∣∣
−1 R3→R3 ∣∣∣100210101∣∣221103∣∣
R1−R3→R1 ∣∣∣100210001∣∣221103∣∣
R1−2R2→R1 ∣∣∣100010001∣∣10721103∣∣
rref A= ∣∣∣100010001∣∣10721103∣∣
⟹x1=107x2=21x3=103
v=107u1+21u2+103u3
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