Math 310, 9am
Quiz 9 solutions: 5.3, 5.4
In C[0,1], with inner product hf, g i=Zb
a
f(x)g(x)dx, find the vector projection of xonto x2.
~p =hf, gi
kgk2g
hf, gi=x, x2=Z1
0
x3dx =1
4
kgk2=hf, f i=x2, x2=Z1
0
x4dx =1
5
∴~p =5
4x2
1
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Solved Problems in Quiz on Applied Linear Algebra | MATH 310, Quizzes of Linear Algebra
Material Type: Quiz; Class: Applied Linear Algebra; Subject: Mathematics; University: University of Illinois - Chicago;
Typology: Quizzes
2011/2012
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Math 310, 9am Quiz 9 solutions: 5.3, 5.
In C[0, 1], with inner product 〈f, g〉 =
∫ (^) b
a
f (x)g(x) dx, find the vector projection of x onto x^2.
~p =
〈f, g〉
‖g‖
2 g
〈f, g〉 =
x, x^2
0
x^3 dx =
‖g‖
2 = 〈f, f 〉 =
x^2 , x^2
0
x
4 dx =
∴ ~p =
x^2