| Condition |
m < n |
m = n |
m > n | |||
|
Show an example of this condition, using - for entries, such
as - - -
- - - for a 2x3 matrix. |
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| Maximum number of pivot columns | ||||||
| Maximum number of pivot rows | ||||||
| p= number of pivot columns | if p=m | if p<m | if p=m | if p<m | if p=n | if p<n |
| 1. Number of solutions of Ax=0
. |
1a | 1b |
1c | 1d | 1e | 1f |
| 2. Number of solutions of Ax=b
where [A|b] has p pivot columns. (Remember, A has p pivot columns). |
2a | 2b | 2c | 2d | 2e | 2f |
| 3. Number of solutions of Ax=b
where [A|b] has p+1 pivot columns (Remember, A has p pivot columns). |
3a | 3b | 3c | 3d | 3e | 3f |
| 4. Is b is in Span{columns of A} for all possible b's? . | 4a | 4b | 4c | 4d | 4e | 4f |
| 5. Do columns of A span R^m?
. |
5a | 5b | 5c | 5d | 5e | 5f |
| 6. Is {Columns of A} linearly independent?
. |
6a | 6b | 6c | 6d | 6e | 6f |