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a) Let V = P3 (R), with an inner product (f.g) = f f(x) g(x) dx. Then for a basis a = {1,x,x², x³), find the matrix representation of an inner product. b) Use Gram-Schmidt orthogonalization process on R4 to convert the basis ((0,1,1,0),(-1,1,0,0), (1,2,0,-1),(-1,0,0,-1)} into an orthonormal basis.

a) Let V = P3 (R), with an inner product (f.g) = f f(x) g(x) dx. Then for a basis a = {1,x,x², x³), find the matrix representation of an inner product. b) Use Gram-Schmidt orthogonalization process on R4 to convert the basis ((0,1,1,0),(-1,1,0,0), (1,2,0,-1),(-1,0,0,-1)} into an orthonormal basis.

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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Answer a and b
a) Let V = P3 (R), with an inner product (f.g) = f(x)g (x) dx. Then for a basis a = {1,x, x², x³}, find the matrix representation of an inner product. b) Use Gram-Schmidt orthogonalization process on R4 to convert the basis {(0,1,1,0), (-1,1,0,0), (1,2,0,-1), (-1,0,0,-1)} into an orthonormal basis.
Transcribed Image Text:a) Let V = P3 (R), with an inner product (f.g) = f(x)g (x) dx. Then for a basis a = {1,x, x², x³}, find the matrix representation of an inner product. b) Use Gram-Schmidt orthogonalization process on R4 to convert the basis {(0,1,1,0), (-1,1,0,0), (1,2,0,-1), (-1,0,0,-1)} into an orthonormal basis.
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