(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find 2 more orthonormal polynomials on the interval [-2,1] up to degree 2 given that the first polynomial p(x) = 1/√3. ( Note: Take the highest coefficient to be positive and enter your answer as a decimal.)

2. Relevant equations

This is a web assign equation so the answer format is in something like this, where I enter in the solutions:

degree 1 = (something)x + something

degree 2 = (something)x^2+(something)x+something

3. The attempt at a solution

I'm trying to understand this problem here. What exactly does the 1 over square root three give us? How does it help?

I was told by my professor that to do this use the dot product of two functions f and g then find integral of f(x)g(x)dx over the boundary conditions. I'm not exactly sure what this means but I followed some examples from the homeworks, as we hadn't really learned this in lecture yet.

So I make up two equations:

f(x) = a + bx

g(x) = x(a+bx)

(1) I integrate both equations on the given boundaries: Int[-2,1] (a + bx) dx= 3a - (3/2)b

(2) INT [-2,1]x(a+bx) dx = -(3/2)a + 3b

After this step I have NO IDEA what to do. I have a system of two equations. I can make a matrix

| 3 -(3/2) |

|-(3/2) 3 |

But how does this help me? If anyone could give me guidance, please do. Thank you very much

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# Homework Help: Infinite dimensions and matrices

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