Let V = span {1+ 2x – x² + 3r³, -2+x +x² – x³, -1+8r – x² + 7r', 3 + x – 2x² + r³}. Find a basis ßfor V that contains the set M = {1+7x – 2x² + 8x³, –1+3x+2r³} . Note: You may assume it has alreadybeen verified that M C V; you need not check this part yourself.%3D

Step:-1 Note:- To span V we need the polynomials of degree 3, so dimension of V is 4. (think using…

Let V = span {1+ 2x – x² + 3r³, -2+x+x² – x*, -1+ 8r – x² + 7r", 3 + x – 2r² + r'}. Find a basis ß for V that contains the set M = {1+7x – 2x² + 8x*, –1+3r+2r³} . Note: You may assume it has already been verified that M C V; you need not check this part yourself.

Let V = span {1+ 2x – x² + 3r³, -2+x+x² – x, -1+ 8r – x² + 7r", 3 + x – 2r² + r'}. Find a basis ß for V that contains the set M = {1+7x – 2x² + 8x, –1+3r+2r³} . Note: You may assume it has already been verified that M C V; you need not check this part yourself.

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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Question

Let V = span {1+ 2x – x² + 3r³, -2+x +x² – x³, -1+8r – x² + 7r', 3 + x – 2x² + r³}. Find a basis ß
for V that contains the set M = {1+7x – 2x² + 8x³, –1+3x+2r³} . Note: You may assume it has already
been verified that M C V; you need not check this part yourself.
%3D

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