I need help on linear algebra 6. Let V = span{1+x²,x}. Two ordered bases for V areSi = {1+a², x}andS2 = {1+x + x², 2+ x + 2a²}.The function f(x) = 5+ 3x + 5x² has component vector5with respect to the basis S1. Find the 2 × 2 change-of-basis matrix Ps,tS1· What is thecomponent vector of f(x) with respect to S2?

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Answered: 6. Let V = span{1+x²,x}. Two ordered…

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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I need help on linear algebra

6. Let V = span{1+x²,x}. Two ordered bases for V are
Si = {1+a², x}
and
S2 = {1+x + x², 2+ x + 2a²}.
The function f(x) = 5+ 3x + 5x² has component vector
5
with respect to the basis S1. Find the 2 × 2 change-of-basis matrix Ps,tS1· What is the
component vector of f(x) with respect to S2?

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.

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