Early homework is due by 5:00 pm Wednesday.
If you did the early homework, you don't need to turn in problems 2 or 5 from section 6.5, problem 11 from section 6.6, or problems 4 or 6 from section 6.7 on Monday. However, please make a note that you have done so. Question 1: Find the least-squares solution to the system:

2 1 -2 0 2 3

x=

-5 8 1

Question 2: Let f(x)= 1 + 4 + 9 + ... + x². It is known that f(x)=a+bx+cx², for real numbers a,b,c. Find, with justification, a system of equations for a,b, and c. [You do not need to solve the system.]
Question 3: Let W=C[0,2&pi] be the space of continuous functions on the inteval [0,2&pi]. (That should be the greek letter "pi", so functions on the interval from 0 to 2pi.)
Endow W with the inner product (f,g)=&int⁰_2&pif(t)g(t)dt. (That should be the integral of fg over the interval from 0 to 2pi.)
Find an orthogonal basis, with respect to this inner product, for the subspace of W spanned by the functions f(t)=sin t and g(t)=cos t. (You may use, without proof, any facts from calculus about definite integrals of trigonometric functions, or the fact that sin 2t=2sintcost.)

---