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Which of the following is (are) a basis of P (R), the space of polynomials with real coefficients of d at most n? (Choose all that apply) O{n} O {1, x,x²,...,x}(degree of increases by 1 up to m) ○ {1, x,x²,..., O {x, x²,..., ,a"}(degree of x increases by 1 up to n) O {2, x, 3x²,..., ,2-1} (degree of increases by 1 up to n - 1) O [25, x, x¹,...,34"}(degree of increases up to 1) O {5, 2x, x², ..., 9a} (degree of increases by 1 up to n) -¹} (degree of increases by 1 up to n − 1)

Which of the following is (are) a basis of P (R), the space of polynomials with real coefficients of d at most n? (Choose all that apply) O{n} O {1, x,x²,...,x}(degree of increases by 1 up to m) ○ {1, x,x²,..., O {x, x²,..., ,a"}(degree of x increases by 1 up to n) O {2, x, 3x²,..., ,2-1} (degree of increases by 1 up to n - 1) O [25, x, x¹,...,34"}(degree of increases up to 1) O {5, 2x, x², ..., 9a} (degree of increases by 1 up to n) -¹} (degree of increases by 1 up to n − 1)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Question:** Which of the following is (are) a basis of \( P_n(\mathbb{R}) \), the space of polynomials with real coefficients of degree at most \( n \)? (Choose all that apply) - [ ] \(\{x^n\}\) - [ ] \(\{1, x, x^2, \ldots, x^n\}\) (degree of \( x \) increases by 1 up to \( n \)) - [ ] \(\{1, x, x^2, \ldots, x^{n-1}\}\) (degree of \( x \) increases by 1 up to \( n-1 \)) - [ ] \(\{x, x^2, \ldots, x^n\}\) (degree of \( x \) increases by 1 up to \( n \)) - [ ] \(\{2, x, 3x^2, \ldots, 2x^{n-1}\}\) (degree of \( x \) increases by 1 up to \( n-1 \)) - [ ] \(\{2x, x^2, x^4, \ldots, 34x^n\}\) (degree of \( x \) increases up to \( n \)) - [ ] \(\{5, 2x, x^2, \ldots, 9x^n\}\) (degree of \( x \) increases by 1 up to \( n \))
Transcribed Image Text:**Question:** Which of the following is (are) a basis of \( P_n(\mathbb{R}) \), the space of polynomials with real coefficients of degree at most \( n \)? (Choose all that apply) - [ ] \(\{x^n\}\) - [ ] \(\{1, x, x^2, \ldots, x^n\}\) (degree of \( x \) increases by 1 up to \( n \)) - [ ] \(\{1, x, x^2, \ldots, x^{n-1}\}\) (degree of \( x \) increases by 1 up to \( n-1 \)) - [ ] \(\{x, x^2, \ldots, x^n\}\) (degree of \( x \) increases by 1 up to \( n \)) - [ ] \(\{2, x, 3x^2, \ldots, 2x^{n-1}\}\) (degree of \( x \) increases by 1 up to \( n-1 \)) - [ ] \(\{2x, x^2, x^4, \ldots, 34x^n\}\) (degree of \( x \) increases up to \( n \)) - [ ] \(\{5, 2x, x^2, \ldots, 9x^n\}\) (degree of \( x \) increases by 1 up to \( n \))
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