Let P' have the inner product given by evaluation at -3,-1,1, and 3. Let P.() =1, p,(1) =t, and p,(1)=r a)Computer the orthogonal projection of P, on to the subspace spanned by P, and P,. b) Find a polynomial q that is orthogonal to P, and P, such tha {P,, pP,-9} is an orthogonal basis for span {Po, P.9} . Scale the polynomial q so that its vector of values at (-3,- 1,1,3) is (1,-1,-1,1) Q#3: Find an orthogonal basis for the column space of the following matrix by Gram-Schmidt Process.

Let P' have the inner product given by evaluation at -3,-1,1, and 3. Let P.() =1, p,(1) =t, and p,(1)=r a)Computer the orthogonal projection of P, on to the subspace spanned by P, and P,. b) Find a polynomial q that is orthogonal to P, and P, such tha {P,, pP,-9} is an orthogonal basis for span {Po, P.9} . Scale the polynomial q so that its vector of values at (-3,- 1,1,3) is (1,-1,-1,1) Q#3: Find an orthogonal basis for the column space of the following matrix by Gram-Schmidt Process.

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

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Let P' have the inner product given by evaluation at -3,-1,1, and 3. Let
P,() =1 , p,(1)=t, and p,(1)=r²
a)Computer the orthogonal projection of P, on to the subspace spanned by P, and P,. b)
Find a polynomial q that is orthogonal to P, and P, such tha {P,, pP,-9} is an orthogonal
basis for span {Po, P,9} . Scale the polynomial q so that its vector of values at (-3,-
1,1,3) is (1,-1,-1,1)
Q#3:
Find an orthogonal basis for the column space of the following matrix by Gram-Schmidt
Process.

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