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27. Row Space example ( Enter your problem )
  1. Example `[[1,-2,0,3,-4],[3,2,8,1,4],[2,3,7,2,3],[-1,2,0,4,-3]]`
  2. Example `[[1,2,3,2],[3,0,1,8],[2,-2,-2,6]]`
  3. Example `[[3,-1,-1],[2,-2,1]]`
  4. 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.
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