Do the polynomials x^3-2x^2+1,4x^2-x+3, and 3x-2 generate P_3(R)?Justify your answer.

mattgondek4 2021-09-18 Answered

Do the polynomials x32x2+1,4x2x+3, and 3x2 generate P3(R)?
Justify your answer.

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Expert Answer

opsadnojD
Answered 2021-09-19 Author has 95 answers
Given polynomials are x32x2+1,4x2x+3 and 3x-2
It is required to find whether they generate P3(R).
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={x32x2+1,4x2x+3} be a subset of P3(R)
The dimension of P3(R) is 4. Every generating set must have at leas n elements.
The given polynomial set S has only three elements. So S cannot generate P3(R)
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