Determine whether b can be written as a linear combination of a₁ and a2. In other words, determine whether weights X₁ and x₂ exist, such that x₁a₁ + x₂a2 = b. Determine theweights x₁ and x₂ if possible.Let a₁ =13 a₂ =-6-4O A. x₁ = 3, x₂ = -5O B.x₁=2, x₂ = -3O C.x₁=2, x₂ = -4OD. There is no solution.and b=182- 16C

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Answered: Determine whether b can be written as a…

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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Question

Determine whether b can be written as a linear combination of a₁ and a2. In other words, determine whether weights X₁ and x₂ exist, such that x₁a₁ + x₂a2 = b. Determine the
weights x₁ and x₂ if possible.
Let a₁ =
1
3 a₂ =
-6
-4
O A. x₁ = 3, x₂ = -5
O B.
x₁=2, x₂ = -3
O C.
x₁=2, x₂ = -4
OD. There is no solution.
and b=
18
2
- 16
C

Expert Solution

Step 1: Introduction of the given problem

$x subscript 1 a subscript 1 plus x subscript 2 a subscript 2 equals b a subscript 1 equals open square brackets table row 1 row 3 row cell negative 6 end cell end table close square brackets a subscript 2 equals open square brackets table row cell negative 4 end cell row 1 row 1 end table close square brackets b equals open square brackets table row 18 row 2 row cell negative 16 end cell end table close square brackets$