Let $ B = \{ 1 + t^2, 1 - t \} $ and $ C = \{ 4, 1 + 5t, t^2 \} $.Does $ B $ form a basis for $ P_2 $?- $ \circ $ Yes, because it has powers of $ t $ from 0 to 2.- $ \circ $ No, because its polynomials are not the standard polynomials $ 1, \, t, $ and $ t^2 $.- $ \circ $ No, because there are not enough vectors in $ B $ to form a basis.- $ \circ $ Yes, because it contains two linearly independent polynomials and $ P_2 $ is two dimensional.If $ q = 26 + 10t + 6t^2 $, find $[q]_C$.\[\begin{bmatrix}\\\\\\\end{bmatrix}\]

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Answered: Let B = {1+t,1 – t} and C = {4, 1 + 5t,…

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Let B = {1+t,1 – t} and C = {4, 1 + 5t, t²}. Does B form a basis for P2?

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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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

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Let $ B = \{ 1 + t^2, 1 - t \} $ and $ C = \{ 4, 1 + 5t, t^2 \} $.

Does $ B $ form a basis for $ P_2 $?

- $ \circ $ Yes, because it has powers of $ t $ from 0 to 2.
- $ \circ $ No, because its polynomials are not the standard polynomials $ 1, \, t, $ and $ t^2 $.
- $ \circ $ No, because there are not enough vectors in $ B $ to form a basis.
- $ \circ $ Yes, because it contains two linearly independent polynomials and $ P_2 $ is two dimensional.

If $ q = 26 + 10t + 6t^2 $, find $[q]_C$.

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