|
27. Row Space example
( Enter your problem )
|
- Example `[[1,-2,0,3,-4],[3,2,8,1,4],[2,3,7,2,3],[-1,2,0,4,-3]]`
- Example `[[1,2,3,2],[3,0,1,8],[2,-2,-2,6]]`
- Example `[[3,-1,-1],[2,-2,1]]`
- Example `[[-2,2,6,0],[0,6,7,5],[1,5,4,5]]`
|
|
4. Example `[[-2,2,6,0],[0,6,7,5],[1,5,4,5]]`
Find Row Space ... `[[-2,2,6,0],[0,6,7,5],[1,5,4,5]]`Solution: | `-2` | `2` | `6` | `0` | | | `0` | `6` | `7` | `5` | | | `1` | `5` | `4` | `5` | |
Now, reduce the matrix to reduced row echelon form `R_1 larr R_1-:(-2)` | = | | `1` | `-1` | `-3` | `0` | | | `0` | `6` | `7` | `5` | | | `1` | `5` | `4` | `5` | |
|
`R_3 larr R_3- R_1` | = | | `1` | `-1` | `-3` | `0` | | | `0` | `6` | `7` | `5` | | | `0` | `6` | `7` | `5` | |
|
`R_2 larr R_2-:6` | = | | `1` | `-1` | `-3` | `0` | | | `0` | `1` | `7/6` | `5/6` | | | `0` | `6` | `7` | `5` | |
|
`R_1 larr R_1+ R_2` | = | | `1` | `0` | `-11/6` | `5/6` | | | `0` | `1` | `7/6` | `5/6` | | | `0` | `6` | `7` | `5` | |
|
`R_3 larr R_3-6xx R_2` | = | | `1` | `0` | `-11/6` | `5/6` | | | `0` | `1` | `7/6` | `5/6` | | | `0` | `0` | `0` | `0` | |
|
The rank of a matrix is the number of non all-zeros rows `:. Rank = 2` Row Space : The nonzero rows in the reduced row-echelon form are a basis for the row space of the matrix `[[1,0,-11/6,5/6]],` `[[0,1,7/6,5/6]]`
This material is intended as a summary. Use your textbook for detail explanation.Any bug, improvement, feedback then Submit Here
|
|
|