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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 (ref)
  2. Transforming matrix to Reduced Row Echelon Form (rref)
  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. Inverse Power Method for dominant eigenvalue
  21. Determinant by gaussian elimination
  22. Expanding determinant along row / column
  23. Determinants using montante (bareiss algorithm)
  24. Leibniz formula for determinant
  25. determinants using Sarrus Rule
  26. determinants using properties of determinants
  27. Row Space
  28. Column Space
  29. Null Space
2. Transforming matrix to Reduced Row Echelon Form (rref)
(Previous method)		2. Example `[[3,2,4],[2,0,2],[4,2,3]]`
(Next example)

1. Example `[[8,-6,2],[-6,7,-4],[2,-4,3]]`


Find Matrix Rank ...
`[[8,-6,2],[-6,7,-4],[2,-4,3]]`

Solution:
 Rank 
`8``-6``2`
`-6``7``-4`
`2``-4``3`


Now, reduce this matrix
`R_2 larr R_2+3/4xx R_1`

 = 
`8``-6``2`
`0``5/2``-5/2`
`2``-4``3`


`R_3 larr R_3-1/4xx R_1`

 = 
`8``-6``2`
`0``5/2``-5/2`
`0``-5/2``5/2`


`R_3 larr R_3+ R_2`

 = 
`8``-6``2`
`0``5/2``-5/2`
`0``0``0`


The rank of a matrix is the number of non all-zeros rows
`:. Rank = 2`


This material is intended as a summary. Use your textbook for detail explanation.
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2. Transforming matrix to Reduced Row Echelon Form (rref)
(Previous method)		2. Example `[[3,2,4],[2,0,2],[4,2,3]]`
(Next example)


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