1. Find the lengths and the inner product of
.
2. For
find a basis for the orthogonal complement to the row space; choose a convenient vector in both of these spaces and verify/demonstrate the orthogonality.
3. Show that if vectors (x-y) and (x+y) in R2 are orthogonal then ||x|| = ||y||.
4. Suppose an n by n matrix in invertible: AA-1 = I. Then the first column of A-1 is orthogonal to the space spanned by which rows of A.
5. Project 
onto the line through 
. Show that b - a is orthogonal to a.
6. Find Ax^ in the column space closest to b for the system
7. Find the least squares line of best fit through the following points:
(t,b) = (-2, 4), (0, 1), (-1, 3)
8. Use Gram-Schmidt method to orthonormalize the basis:
