Find the solution vectors u and v such that the solution space is the set of all linear combinations of the form su + tv. X₁ -3x2 + x3 - 11x4 = 0 X₁ + 2x₂ + x3 + 19 ×4 = 0 X₁ + X₂ + x3 +13 X4 = 0 The solution vectors are u = and v= such that x = su + tv, x3 =s and x4=t, where s and t are real numbers.

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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Find the solution vectors u and v such that the solution space is the set of all linear combinations of the form su + tv.
X₁ - 3 x₂ + x3
- 11x4 = 0
+ 19 X4
x2 + x3 + 13x4
X₁ + 2x₂ + x3
x₁ +
The solution vectors are u =
= 0
= 0
and v=
such that x = su + tv, x3 = s and x4 = t, where s and t are real numbers.
Transcribed Image Text:Find the solution vectors u and v such that the solution space is the set of all linear combinations of the form su + tv. X₁ - 3 x₂ + x3 - 11x4 = 0 + 19 X4 x2 + x3 + 13x4 X₁ + 2x₂ + x3 x₁ + The solution vectors are u = = 0 = 0 and v= such that x = su + tv, x3 = s and x4 = t, where s and t are real numbers.
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