|
|
Home > Matrix & Vector calculators > Row Space example
|
|
22. 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]]`
|
Other related methods
- Transforming matrix to Row Echelon Form
- Transforming matrix to Reduced Row Echelon Form
- Rank of matrix
- Characteristic polynomial of matrix
- Eigenvalues
- Eigenvectors (Eigenspace)
- Triangular Matrix
- LU decomposition using Gauss Elimination method of matrix
- LU decomposition using Doolittle's method of matrix
- LU decomposition using Crout's method of matrix
- Diagonal Matrix
- Cholesky Decomposition
- QR Decomposition (Gram Schmidt Method)
- QR Decomposition (Householder Method)
- LQ Decomposition
- Pivots
- Singular Value Decomposition (SVD)
- Moore-Penrose Pseudoinverse
- Power Method for dominant eigenvalue
- determinants using Sarrus Rule
- determinants using properties of determinants
- Row Space
- Column Space
- Null Space
|
|
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
|
|
|
|
Share this solution or page with your friends.
|
|
|
|