V = P2, W = {a + bx + ca2la+b+c=0}. %3D

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter12: Quadratic Functions
Section12.2: Completing The Square
Problem 29WE
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Determine if W is a subspace of V:

V = P2, W = {a + bx + ca2la+b+c=0}.
%3D
Transcribed Image Text:V = P2, W = {a + bx + ca2la+b+c=0}. %3D
Expert Solution
Step 1

To show that W is a subspace of V, check the 3 conditions.

  1. Zero vector is in W.
  2. Closed under addition.
  3. Closed under scalar multiplication.
Step 2

1) Clearly, the zero vector 0 is in W. Since it is the element with a=b=c=0 and satisfies a + b + c = 0. Hence the first condition satisfied.

Step 3

Check the second condition.

Advanced Math homework question answer, step 3, image 1

Step 4

Advanced Math homework question answer, step 4, image 1

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