Do the polynomials

Justify your answer.

mattgondek4
2021-09-18
Answered

Do the polynomials

Justify your answer.

You can still ask an expert for help

opsadnojD

Answered 2021-09-19
Author has **95** answers

Given polynomials are ${x}^{3}-2{x}^{2}+1,4{x}^{2}-x+3$ and 3x-2

It is required to find whether they generate${P}_{3}\left(R\right)$ .

Answer is No.

It is known that the vector space P3(R) consists of all polynomials having degree less than or equal to 3.

Let$S=\{{x}^{3}-2{x}^{2}+1,4{x}^{2}-x+3\}$ be a subset of ${P}_{3}\left(R\right)$

The dimension of${P}_{3}\left(R\right)$ is 4. Every generating set must have at leas n elements.

The given polynomial set S has only three elements. So S cannot generate${P}_{3}\left(R\right)$

It is required to find whether they generate

Answer is No.

It is known that the vector space P3(R) consists of all polynomials having degree less than or equal to 3.

Let

The dimension of

The given polynomial set S has only three elements. So S cannot generate

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