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Exercise 6.3.6 Exhibit a basis and calculate the dimen- sion of each of the following subspaces of P2. a. {a(1+x)+b(x+x²) | a and b in R} b. {a+b(x+x²) | a and b in R} c. {p(x) | p(1)=0} d. {p(x)|p(x) = p(−x)}

Exercise 6.3.6 Exhibit a basis and calculate the dimen- sion of each of the following subspaces of P2. a. {a(1+x)+b(x+x²) | a and b in R} b. {a+b(x+x²) | a and b in R} c. {p(x) | p(1)=0} d. {p(x)|p(x) = p(−x)}

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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Exercise 6.3.6 Exhibit a basis and calculate the dimen- sion of each of the following subspaces of P2. a. {a(1+x)+b(x+x²) | a and bin R} b. {a+b(x+x²) | a and bin R} c. {p(x) |p(1) = 0} d. {p(x)|p(x) = p(-x)} Exercise 6.3.7 Exhibit a basis and calculate the dimen- sion of each of the following subspaces of M22. a. {A|AT = -A} D. {^|^| _¦ ¦ | -|_|₁} {A|A b. А Exer or gi a. b.
Transcribed Image Text:Exercise 6.3.6 Exhibit a basis and calculate the dimen- sion of each of the following subspaces of P2. a. {a(1+x)+b(x+x²) | a and bin R} b. {a+b(x+x²) | a and bin R} c. {p(x) |p(1) = 0} d. {p(x)|p(x) = p(-x)} Exercise 6.3.7 Exhibit a basis and calculate the dimen- sion of each of the following subspaces of M22. a. {A|AT = -A} D. {^|^| _¦ ¦ | -|_|₁} {A|A b. А Exer or gi a. b.
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