4. Consider the following subset of P3, i.e., the vector space of polynomials of degree < 3: W = {p(t) € P3|p(1) = p'(2) = 0} . (a) Prove that W is a subspace of P3. (b) Find a basis for W. (c) Find the dimension of W.

4. Consider the following subset of P3, i.e., the vector space of polynomials of degree < 3: W = {p(t) € P3|p(1) = p'(2) = 0} . (a) Prove that W is a subspace of P3. (b) Find a basis for W. (c) Find the dimension of W.

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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4. Consider the following subset of P3, i.e., the vector space of polynomials of degree < 3:
W = {p(t) € P3|p(1) = p'(2) = 0} .
(a) Prove that W is a subspace of P3.
(b) Find a basis for W.
(c) Find the dimension of W.

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