### Problem Statement:Determine which of the following sets is a subspace of $ P_n $ for an appropriate value of $ n $.#### Options:1. **A:** All polynomials of the form $ p(t) = a + bt^2 $, where $ a $ and $ b $ are in $ \mathbb{R} $2. **B:** All polynomials of degree exactly 4, with real coefficients.3. **C:** All polynomials of degree at most 4, with positive coefficients.#### Answer Choices:- A) A and B- B) B only- C) A only- D) C only

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Šolve the problem. 1) Determine which of the following sets is a subspace of Pn for an appropriate value of n. A: All polynomials of the form p(t) = a + bt2, where a and b are in R B: All polynomials of degree exactly 4, with real coefficients C: All polynomials of degree at most 4, with positive coefficients A) A and B B) B only C) A only D) C only

Šolve the problem. 1) Determine which of the following sets is a subspace of Pn for an appropriate value of n. A: All polynomials of the form p(t) = a + bt2, where a and b are in R B: All polynomials of degree exactly 4, with real coefficients C: All polynomials of degree at most 4, with positive coefficients A) A and B B) B only C) A only D) C only

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.

Question

### Problem Statement:

Determine which of the following sets is a subspace of $ P_n $ for an appropriate value of $ n $.

#### Options:

1. **A:** All polynomials of the form $ p(t) = a + bt^2 $, where $ a $ and $ b $ are in $ \mathbb{R} $
2. **B:** All polynomials of degree exactly 4, with real coefficients.
3. **C:** All polynomials of degree at most 4, with positive coefficients.

#### Answer Choices:

- A) A and B
- B) B only
- C) A only
- D) C only

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