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 ]>

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Description: 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 th

Answered: Consider the ordered basis 3 = {1, 1+…

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 ]
>

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

Expert Solution

Step 1

Given $β = \{1, 1 + x, 1 + x + x^{2}\}$

And ${[1 + 2 x + 3 x^{2}]}_{β} = {(a, b, c)}^{t}$

We have to find value for $a, b a n d c$

$\begin{array}{l} \Rightarrow 1 + 2 x + 3 x^{2} = a \cdot 1 + b (1 + x) + c (1 + x + x^{2}) \\ \Rightarrow 1 + 2 x + 3 x^{2} = a + b + b x + c + c x + c x^{2} \\ \Rightarrow 1 + 2 x + 3 x^{2} = (a + b + c) + (b + c) x + c x^{2} \end{array}$

Compare both sides, we get

$\begin{matrix} a + b + c = 1...... (1) \\ b + c = 2...... (2) \\ c = 3...... (3) \end{matrix}$

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