Determine whether each of the following sets is a basis for P2. Justify your answer ineach case1.i.A = {1+t,t + t2}(, (い+) +(, Cト+):0ioicっこ0is lineorly independlentAformsB = {t² + 7,2t - 3, t + 5, t2 +t + 1}basis for P?.ii.iii.B = {1-t,-1+ 2t?, 1- 2t + t?}

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Determine whether each of the following sets is a basis for P2. Justify your answer in each case i. 1. A = {1+t,t+ t2} (ト +) =0 =01(2 =0 is lineorly forms inde pendent ba sis for Pz, B = {t? + 7,2t - 3,t + 5, t2 + t + 1} A ii. iii. B = {1 - t,-1+ 2t?, 1- 2t + t²}

Determine whether each of the following sets is a basis for P2. Justify your answer in each case i. 1. A = {1+t,t+ t2} (ト +) =0 =01(2 =0 is lineorly forms inde pendent ba sis for Pz, B = {t? + 7,2t - 3,t + 5, t2 + t + 1} A ii. iii. B = {1 - t,-1+ 2t?, 1- 2t + t²}

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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Concept explainers

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.

Question

Determine whether each of the following sets is a basis for P2. Justify your answer in
each case
1.
i.
A = {1+t,t + t2}
(, (い+) +(, Cト+):0
ioicっこ0
is lineorly inde
pendlent
A
forms
B = {t² + 7,2t - 3, t + 5, t2 +t + 1}
basis for P?.
ii.
iii.
B = {1-t,-1+ 2t?, 1- 2t + t?}

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