Question

Let P3 be the vector space of all polynomials with real coefficients of degree at most 3. Determine whether the given set is a subspace of P3 or not. (a) H = {1 + t^2} (b) H = {polynomials p(t) with p(3) = 0}

Name: let p3 be the vector space of all polynomials with real coefficients of degree at most 3 determine whether the given set is a subspace of p3 or not a h1t2 b hpolynomials pt with p30 69057
Uploaded: 2022-08-17T07:56:24-08:00
Duration: 4 min 42 s
Channel: Adi S
Description: let p3 be the vector space of all polynomials with real coefficients of degree at most 3 determine whether the given set is a subspace of p3 or not a h1t2 b hpolynomials pt with p30 69057

          Let P3 be the vector space of all polynomials with real coefficients of degree at most 3. Determine whether the given set is a subspace of P3 or not.
(a) H = {1 + t^2}
(b) H = {polynomials p(t) with p(3) = 0}

Added by Angela W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

08/17/2022

Step 1

Since the zero polynomial is not in \(H\) (as \(1 \neq 0\)), \(H\) does not contain the zero vector required for it to be a subspace. Therefore, \(H\) is not a subspace of \(P3\). **Step 2:** For part (b) where \(H = \{p(t) \mid p(3) = 0\}\), we need to Show more…

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Let P3 be the vector space of all polynomials with real coefficients of degree at most 3. Determine whether the given set is a subspace of P3 or not. (a) H = {1 + t^2} (b) H = {polynomials p(t) with p(3) = 0}