Answer to Question #159351 in Linear Algebra for Abhipsita Das

Question

Find all solutions to the following system of linear equations.

x1 − x2 − x3 = 2

2x1 + x2 + 2x3 = 4

x1 − 4x2 − 5x3 = 2

Answer 1

X₁-X₂-X₃=2

2X₁+X₂+2X₃=4

X_1-4X₂-5X₃=2

Making X₁ the subject of the formula

X₁=2+X₂+X₃

2(2+X₂+X₃) +X₂+2X₃=4

4+2X₂+2 X₃+ X₂+2X₃=4

Collecting the like terms

3 X₂+4 X₃=4-4

3X₂=-4X₃

X₃=-4/3X₃...(i)

2+X₂+X₃-4X₂-5X₃=2

Collecting the like terms

X₃-5X₃-4X₂+ X₂=2-2

-4 X₃-3 X₂=0

3X₂=-4X₃

X₂=-4/3X₃...(ii)

∴ -4/3X₃=-4/3X₃

X₃=0 and X₂=0

X₁=2+0+0

X₁=2

∴ X₁=2, X₂=0, and X₃=0