Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Linear Algebra
In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied unde…
Question

let p(x) = a0+a1x+a2x2 and  q(x) = b0+b1x+b2x2

be vectors in P2 with inner product <p,q> = a0b0+a1b1+a2b2

Consider the polynomials in the set {−1+x2,2+x+x2}

Show that the polynomials in the set do not form an orthonormal set.

Use the Gram-Schmidt orthonormalization process to form an orthonormal set from these polynomials. Keep the order, and show work for the orthogonalization, then normalization.

Do the polynomials in the orthonormal set (from question 2) form a basis for P2 ? Why or why not?

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