Consider the ordered basis 3 = {1, 1+ x, 1+ x + x²}. Given that %3D [1+ 2л + За?]8 — (а, b, с)*, choose the correct values for a, b, and c below: a equals [Select ] b equals [Select ] C eguals [Select ] >

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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Hi, I need help with this Linear Algebra exercise, please. Thank you!

Drop drop menu for answers are: -3,-2,-1,0,1,2,3 for all 3 questions.

Consider the ordered basis B = {1, 1+x, 1+ x + x²}. Given that
[1 + 2 + За?]8 %3 (а, b, с)*,
(a, b, c)*,
choose the correct values for a, b, and cbelow:
a equals [Select ]
b equals [ Select ]
• c equals [ Select ]
>
Transcribed Image Text:Consider the ordered basis B = {1, 1+x, 1+ x + x²}. Given that [1 + 2 + За?]8 %3 (а, b, с)*, (a, b, c)*, choose the correct values for a, b, and cbelow: a equals [Select ] b equals [ Select ] • c equals [ Select ] >
Expert Solution
Step 1

Given β=1,1+x,1+x+x2

And 1+2x+3x2β=a,b,ct

We have to find value for a,b and c

1+2x+3x2=a1+b1+x+c1+x+x21+2x+3x2=a+b+bx+c+cx+cx21+2x+3x2=a+b+c+b+cx+cx2

Compare both sides, we get

a+b+c=1......1b+c=2......2c=3......3

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