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3. Consider the set S {1x², -x + 2x2,1 + 2x - x²} in P2 (R). Attempting to find a linear dependence is equivalent to finding a non-trivial solution (a, b, c) to a system of linear equations = a(1-x²) + b(-x+ 2x²) + c(1 + 2x - x²) = =0⇒>> (0 0 0) 11 a+c=0 -b+2c=0 -a +2b-c=0 C:

3. Consider the set S {1x², -x + 2x2,1 + 2x - x²} in P2 (R). Attempting to find a linear dependence is equivalent to finding a non-trivial solution (a, b, c) to a system of linear equations = a(1-x²) + b(-x+ 2x²) + c(1 + 2x - x²) = =0⇒>> (0 0 0) 11 a+c=0 -b+2c=0 -a +2b-c=0 C:

Advanced Engineering Mathematics
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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Please do it by using matrix. Thank you!

3. Consider the set S {1 − x², −x + 2x²,1 + 2x − x²} in P₂ (R). Attempting to find a linear dependence is equivalent to finding a non-trivial solution (a, b, c) to a system of linear equations = a(1-x²)+b(-x+ 2x²) + c(1 + 2x - x²) = 0 ⇒ a+c=0 -b+2c=0 -a +2b-c=0 Since the only solution is trivial (a, b, c) = (0,0,0), the set S is linearly independent.
Transcribed Image Text:3. Consider the set S {1 − x², −x + 2x²,1 + 2x − x²} in P₂ (R). Attempting to find a linear dependence is equivalent to finding a non-trivial solution (a, b, c) to a system of linear equations = a(1-x²)+b(-x+ 2x²) + c(1 + 2x - x²) = 0 ⇒ a+c=0 -b+2c=0 -a +2b-c=0 Since the only solution is trivial (a, b, c) = (0,0,0), the set S is linearly independent.
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