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Home > Matrix & Vector calculators > Rank of matrix example
3. Rank of matrix example ( Enter your problem )
( Enter your problem )
  1. Example `[[8,-6,2],[-6,7,-4],[2,-4,3]]`
  2. Example `[[3,2,4],[2,0,2],[4,2,3]]`
  3. Example `[[1,1,1],[-1,-3,-3],[2,4,4]]`
  4. Example `[[2,3],[4,10]]`
 		Other related methods
  1. Transforming matrix to Row Echelon Form
  2. Transforming matrix to Reduced Row Echelon Form
  3. Rank of matrix
  4. Characteristic polynomial of matrix
  5. Eigenvalues
  6. Eigenvectors (Eigenspace)
  7. Triangular Matrix
  8. LU decomposition using Gauss Elimination method of matrix
  9. LU decomposition using Doolittle's method of matrix
  10. LU decomposition using Crout's method of matrix
  11. Diagonal Matrix
  12. Cholesky Decomposition
  13. QR Decomposition (Gram Schmidt Method)
  14. QR Decomposition (Householder Method)
  15. LQ Decomposition
  16. Pivots
  17. Singular Value Decomposition (SVD)
  18. Moore-Penrose Pseudoinverse
  19. Power Method for dominant eigenvalue
  20. determinants using Sarrus Rule
  21. determinants using properties of determinants
  22. Row Space
  23. Column Space
  24. Null Space
1. Example `[[8,-6,2],[-6,7,-4],[2,-4,3]]`
(Previous example)		3. Example `[[1,1,1],[-1,-3,-3],[2,4,4]]`
(Next example)

2. Example `[[3,2,4],[2,0,2],[4,2,3]]`


Find Rank of matrix ...
`[[3,2,4],[2,0,2],[4,2,3]]`

Solution:
 Rank 
`3``2``4`
`2``0``2`
`4``2``3`


Now, reduce this matrix
`R_1 larr R_1-:3`

 = 
 `1` `1=3-:3`
`R_1 larr R_1-:3`		 `2/3` `2/3=2-:3`
`R_1 larr R_1-:3`		 `4/3` `4/3=4-:3`
`R_1 larr R_1-:3`
`2``0``2`
`4``2``3`


`R_2 larr R_2-2xx R_1`

 = 
`1``2/3``4/3`
 `0` `0=2-2xx1`
`R_2 larr R_2-2xx R_1`		 `-4/3` `-4/3=0-2xx2/3`
`R_2 larr R_2-2xx R_1`		 `-2/3` `-2/3=2-2xx4/3`
`R_2 larr R_2-2xx R_1`
`4``2``3`


`R_3 larr R_3-4xx R_1`

 = 
`1``2/3``4/3`
`0``-4/3``-2/3`
 `0` `0=4-4xx1`
`R_3 larr R_3-4xx R_1`		 `-2/3` `-2/3=2-4xx2/3`
`R_3 larr R_3-4xx R_1`		 `-7/3` `-7/3=3-4xx4/3`
`R_3 larr R_3-4xx R_1`


`R_2 larr R_2xx-3/4`

 = 
`1``2/3``4/3`
 `0` `0=0xx-3/4`
`R_2 larr R_2xx-3/4`		 `1` `1=-4/3xx-3/4`
`R_2 larr R_2xx-3/4`		 `1/2` `1/2=-2/3xx-3/4`
`R_2 larr R_2xx-3/4`
`0``-2/3``-7/3`


`R_3 larr R_3+2/3xx R_2`

 = 
`1``2/3``4/3`
`0``1``1/2`
 `0` `0=0+2/3xx0`
`R_3 larr R_3+2/3xx R_2`		 `0` `0=-2/3+2/3xx1`
`R_3 larr R_3+2/3xx R_2`		 `-2` `-2=-7/3+2/3xx1/2`
`R_3 larr R_3+2/3xx R_2`


`R_3 larr R_3-:-2`

 = 
`1``2/3``4/3`
`0``1``1/2`
 `0` `0=0-:-2`
`R_3 larr R_3-:-2`		 `0` `0=0-:-2`
`R_3 larr R_3-:-2`		 `1` `1=-2-:-2`
`R_3 larr R_3-:-2`


The rank of a matrix is the number of non all-zeros rows
`:. Rank = 3`

This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then Submit Here


1. Example `[[8,-6,2],[-6,7,-4],[2,-4,3]]`
(Previous example)		3. Example `[[1,1,1],[-1,-3,-3],[2,4,4]]`
(Next example)


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