Find a basis for the orthogonal complement to the row space

Question

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: