In: Advanced Math
Given the following utility matrix, representing the ratings, on a 1–5 star scale, of eight items, a through h, by three users A, B, and C:
| a | b | c | d | e | f | g | h | |
| A | 4 | 5 | 5 | 1 | 3 | 2 | ||
| B | 3 | 4 | 3 | 1 | 2 | 1 | ||
| C | 2 | 1 | 3 | 4 | 5 | 3 | 
After we normalize the matrix by subtracting from each nonblank entry the average value for its user, what is the cosine distance between users A and C ?
| 
 -0.1155  | 
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| 
 0.5842  | 
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| 
 0.3334  | 
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| 
 -0.7396  |