Take L: V --> W, from P2 --> P2 and L(p) = p + p', with basis B = {1 + x + x2, 1 + x, 2x + x2} and basis C = {1 + x, x - x2, 3 + x2}. Find [x]B, [x]C, [Id] from basis B to C, and [Id] from basis C to B. Show that L is linear

Take L: V --> W, from P2 --> P2 and L(p) = p + p', with basis B = {1 + x + x2, 1 + x, 2x + x2} and basis C = {1 + x, x - x2, 3 + x2}. Find [x]B, [x]C, [Id] from basis B to C, and [Id] from basis C to B. Show that L is linear

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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Take L: V --> W, from P₂ --> P₂ and L(p) = p + p', with basis B = {1 + x + x², 1 + x, 2x + x²} and basis C = {1 + x, x - x², 3 + x²}. Find [x]_B, [x]_C, [Id] from basis B to C, and [Id] from basis C to B. Show that L is linear.

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