Question
Download Solution PDFLet l ≥ 1 be a positive integer. What is the dimension of the ℝ-vector space of all polynomials in two variables over R having a total degree of at most l?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Dimension of the vector space of polynomial f of m variable having degree at most n is \(^{m+n}C_m\)
Explanation:
Here number of variable of polynomial is 2 and degree is at most l so
dimension = \(^{l+2}C_2\) = \(\frac{(l+2)!}{2!\times l!}\) = \(\frac{(l+2)(l+1)\times l!}{2\times l!}\) = (l + 1)(l + 2)/2
Option (4) is correct
Last updated on Jun 5, 2025
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