Do the polynomials ${x}^{3}-2{x}^{2}+1,4{x}^{2}-x+3$, and $3x-2$ generate ${P}_{3}\left(R\right)$?

You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

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 ${P}_{3}\left(R\right)$.
It is known that the vector space P3(R) consists of all polynomials having degree less than or equal to 3.
Let $S=\left\{{x}^{3}-2{x}^{2}+1,4{x}^{2}-x+3\right\}$ 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 ${P}_{3}\left(R\right)$
###### Not exactly what you’re looking for?

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee