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Home > Matrix & Vector calculators > Determinants using Sarrus Rule example
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20. determinants using Sarrus Rule example
( Enter your problem )
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- Example `[[1,2,3],[4,5,6],[7,8,9]]`
- Example `[[3,2,4],[2,0,2],[4,2,3]]`
- Example `[[1,1,1],[-1,-3,-3],[2,4,4]]`
- Example `[[1,2,3],[0,1,0],[2,3,1]]`
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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
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1. Example `[[1,2,3],[4,5,6],[7,8,9]]`
1. Find determinants using Sarrus Rule ...
`[[1,2,3],[4,5,6],[7,8,9]]`
Solution:
Write first 2 columns of matrix to right of 3rd column, so we have total 5 columns.
| `A=` | | 1 | 2 | 3 | 1 | 2 | | | 4 | 5 | 6 | 4 | 5 | | | 7 | 8 | 9 | 7 | 8 | |
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| `A=` | | 1 | 2 | 3 | 1 | 2 | | | 4 | 5 | 6 | 4 | 5 | | | 7 | 8 | 9 | 7 | 8 | |
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Now, add products of diagonals going from top to bottom (blue lines) and subtract products of diagonals going from bottom to top (red lines).
`={1*5*9+2*6*7+3*4*8}-{7*5*3+8*6*1+9*4*2}`
`=(45+84+96)-(105+48+72)`
`=225-225`
`=0`
This material is intended as a summary. Use your textbook for detail explanation.
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