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

mattgondek4

mattgondek4

Answered question

2021-09-18

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

Answer & Explanation

opsadnojD

opsadnojD

Skilled2021-09-19Added 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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