Question

The set B = 1 + x 2 , x + x 2 , 1 + 2x + x 2 is a basis for P2(R). Find the coordinate vector of p(x) = 1 + 3x − 6x 2 relative to B.

Name: the set b 1 x 2 x x 2 1 2x x 2 is a basis for p2r find the coordinate vector of px 1 3x 6x 2 relative to b 50588
Uploaded: 2019-08-12T23:58:08-08:00
Duration: 1 min 48 s
Channel: Doruk Isik
Description: the set b 1 x 2 x x 2 1 2x x 2 is a basis for p2r find the coordinate vector of px 1 3x 6x 2 relative to b 50588

          The set B =
1 + x
2
, x + x
2
, 1 + 2x + x
2
is a basis for P2(R). Find the coordinate vector
of p(x) = 1 + 3x − 6x
2
relative to B.

Added by Christopher L.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Doruk Isik

08/12/2019

Step 1

Let's denote the elements of \( B \) as follows: \[ b_1 = 1 + x^2 \] \[ b_2 = x + x^2 \] \[ b_3 = 1 + 2x + x^2 \] We need to find constants \( c_1, c_2, c_3 \) such that: \[ p(x) = c_1 b_1 + c_2 b_2 + c_3 b_3 \] Substituting the expressions for \( b_1, b_2, b_3 Show more…

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