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27. Row Space example
( Enter your problem )
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- 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]]`
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3. Example `[[3,-1,-1],[2,-2,1]]`
Find Row Space ...
`[[3,-1,-1],[2,-2,1]]`Solution:Now, reduce the matrix to reduced row echelon form `R_1 larr R_1-:3` | = | | `1` | `-1/3` | `-1/3` | | | `2` | `-2` | `1` | |
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`R_2 larr R_2-2xx R_1` | = | | `1` | `-1/3` | `-1/3` | | | `0` | `-4/3` | `5/3` | |
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`R_2 larr R_2xx(-3/4)` | = | | `1` | `-1/3` | `-1/3` | | | `0` | `1` | `-5/4` | |
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`R_1 larr R_1+1/3xx R_2` 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,-3/4]],` `[[0,1,-5/4]]`
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