6. Find the solutions by Inverse Matrix method If AX-Y and D 0, then X-A¹Y (1) (3x, -6x, = 0 (2x₁-5x₂=-1 (2) -2x+3x, 4 5x,-4x₂ =-3 x₁ - x₂ + x₁ =1 (3) ₁-2x₂ + x₁ =2 (x₂-3x₂ + x₂ =3

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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6. Find the solutions by Inverse Matrix method
If AX = Y and D÷0, then X = A-¹Y
(1)
[3x₁-6x₂ = 0
|2x₁ -5x₂ = -1
2x₁ + x₂-x₂=5
(4) x₂-3x₂ + x₂ = 2
(x₁+3x₂-3x₂
= 0
(2)
5x,-4x₂=-3
X₁ X₂ + x₁ = 1
(3) ₁-2x₂+x₂=2
(x₂-3x₂ + x₂ =3
[2x₁ + x₂ + 2x₂=1
(5) x₂ + x₁ =-1
(-x₂+2x₂-2x, = -3
[x₂ + x₂ + x₁ = 2
(6) 2x, -5x, +3x, = 5
[-x₁ + 2x₂ + x₂ = 0
Transcribed Image Text:6. Find the solutions by Inverse Matrix method If AX = Y and D÷0, then X = A-¹Y (1) [3x₁-6x₂ = 0 |2x₁ -5x₂ = -1 2x₁ + x₂-x₂=5 (4) x₂-3x₂ + x₂ = 2 (x₁+3x₂-3x₂ = 0 (2) 5x,-4x₂=-3 X₁ X₂ + x₁ = 1 (3) ₁-2x₂+x₂=2 (x₂-3x₂ + x₂ =3 [2x₁ + x₂ + 2x₂=1 (5) x₂ + x₁ =-1 (-x₂+2x₂-2x, = -3 [x₂ + x₂ + x₁ = 2 (6) 2x, -5x, +3x, = 5 [-x₁ + 2x₂ + x₂ = 0
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