MATH 311 Lecture Notes - Lecture 6: Dot Product, Unit Vector, Orthogonality

For sine and cosine functions, our orthogonality conditions arc: Derive these three results by hand. (Hint: you may need to use trigonometry identities and you may need to use integration by parts)

0 1 Problem 26 Consider matrices -10 1 0 1. Find the eigenvalues and normalized eigenvectors of these matrices. 2. Check orthogonality of the found vectors.

4. (10 points) Let two vectors?-(x1,22, ,xn) and у : (yī,12 yn). a) Provide definition of orthogonality. b) Prove that if # and are mutually orthogonal, then they are linearly independent.