Class 27

eigenvalues and eigenvectors continued; diagonalization (Sections 6.2)
Problems:
- - ```
  for the  matrix
  A= [  cos(theta) -sin(theta) ]
     [  sin(theta)  cos(theta) ]
```
- ```
for
B= [   0  1  ]
   [  -1  0  ]
```
- John and Mary are taking linear algebra. One of the problems in their homework assignment was to find the nullspace of the 4X5 matrix A. John's answer was that the nullspace is spanned by (-2, -2, 0, 2, -6), (1, 5, 4, -3, 11), (3, 5, 2, -4, 13), and (0, -2, -2, 1, -4). Mary's answer was that the nullspace is spanned by (1, 1, 0, -1, 3), (-2, 0, 2, 1, -2), and (-1, 3, 4, 1, 5). Are their answers consistent with each other? (See this directory for matlab and diary files with solution.)