3. Solve the following linear systems by Gauss-Jordan method: a) x₁ + x₂ - 2x3 + x4 = -1 b) - x₁ + x₂ + x3 - 2x4 x5 = 0 x₁ + 2x₂ - x₁ = -4 3x₁ - 3x₂-x3 + 2x₁ + x₂ = 1 - X₁ + X₂ X3 + x₁ = 4 x₁ - x₂ - 2x₂ + 3x4 + 2x5 = 1 2x₁ - x₂ + x3 - 2x₁ = -10 - 3x₂ + x₂ + x₁ = 5 c) 2x, +3x₂-10x3 - 4x4 - 4x = 1 3x₁ - x₂-9x3 +5x4-2x = -2 -x₁ +4x₂-x₂-9x₁-2x, = 9 d) x₁ + 2x₂ + 4x₂ = 1 - x₁ - 3x₂ - x₂ = 3 2x₁ +5x₂ + 5x3 = -2 3x₁ + 7x₂ +9x3 = -1
3. Solve the following linear systems by Gauss-Jordan method: a) x₁ + x₂ - 2x3 + x4 = -1 b) - x₁ + x₂ + x3 - 2x4 x5 = 0 x₁ + 2x₂ - x₁ = -4 3x₁ - 3x₂-x3 + 2x₁ + x₂ = 1 - X₁ + X₂ X3 + x₁ = 4 x₁ - x₂ - 2x₂ + 3x4 + 2x5 = 1 2x₁ - x₂ + x3 - 2x₁ = -10 - 3x₂ + x₂ + x₁ = 5 c) 2x, +3x₂-10x3 - 4x4 - 4x = 1 3x₁ - x₂-9x3 +5x4-2x = -2 -x₁ +4x₂-x₂-9x₁-2x, = 9 d) x₁ + 2x₂ + 4x₂ = 1 - x₁ - 3x₂ - x₂ = 3 2x₁ +5x₂ + 5x3 = -2 3x₁ + 7x₂ +9x3 = -1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:3. Solve the following linear systems by Gauss-Jordan method:
a) x₁ + x₂ - 2x₂ + x₁ = -1
b) - x₁ + x₂ + x3 2x4xX5 = 0
x₂ + 2x₂
-x4 = -4
3x₁3x₂-x₂+2x₁ + x = 1
-x₁ + x₂-x₂ + x₁ = 4
x₁ - x₂ - 2x₂ + 3x₂ + 2x₂ = 1
2x₁ - x₂ + x3
2x4 = -10
- 3x₂ + x₂ + x₁ = 5
c)
2x, +3x₂ -10x3 - 4x4 - 4x5=1
3x₁ − x₂ −9x3 +5x₁ − 2x₁ = −2
-x₁ +4x₂-x3-9x4-2x5=9
d)
x₁ + 2x₂ + 4x₂ = 1
-x₁ - 3x₂ - x₂ = 3
2x₁ +5x₂ + 5x3 = -2
3x₁ + 7x₂ +9x₂ = -1
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