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28. Column 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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4. Example `[[-2,2,6,0],[0,6,7,5],[1,5,4,5]]`
Find Column 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 row echelon form `R_3 larr R_3+1/2xx R_1` | = | | `-2` | `2` | `6` | `0` | | | `0` | `6` | `7` | `5` | | | `0` | `6` | `7` | `5` | |
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`R_3 larr R_3- R_2` | = | | `-2` | `2` | `6` | `0` | | | `0` | `6` | `7` | `5` | | | `0` | `0` | `0` | `0` | |
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The rank of a matrix is the number of non all-zeros rows `:. Rank = 2` Column Space : The matrix has 2 pivots and Pivots are in the columns 1 and 2. We know that these columns in the original matrix define the column space of the matrix. `:.` The Column Space is `[[-2],[0],[1]],[[2],[6],[5]]`
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