Determine whether b can be written as a linear combination of a, 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 -6 a₂ = <-4 1 1 O A. x₁ = 3, x₂ = -5 OB. x₁ = 2, x₂ = -3 OC. x₁ = 2, x₂ = -4 OD. There is no solution. and b= 18 2 - 16

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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
Transcribed Image Text: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

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