|
|
|
|
Code is changed on 22.07.2025, Now it also works for Complex Number.
For wrong or incomplete solution, please submit the feedback form.
So, I will try my best to improve it soon.
|
|
|
|
|
|
|
Solution
|
Solution provided by AtoZmath.com
|
|
|
|
determinants using Sarrus Rule calculator
|
 1. `[[8,-6,2],[-6,7,-4],[2,-4,3]]`
2. `[[3,2,4],[2,0,2],[4,2,3]]`
3. `[[1,1,1],[-1,-3,-3],[2,4,4]]`
4. `[[1,2,3],[0,1,0],[2,3,1]]`
5. `[[1,2,1],[6,-1,0],[-1,-2,-1]]`
6. `[[6,-2,2],[-2,3,-1],[2,-1,3]]`
|
Example1. 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 | |
|
| `A=` | | 1 | 2 | 3 | 1 | 2 | | | 4 | 5 | 6 | 4 | 5 | | | 7 | 8 | 9 | 7 | 8 | |
|
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` Method-2: Determinant by expanding cofactors| `|A|` | = | | `1` | `2` | `3` | | | `4` | `5` | `6` | | | `7` | `8` | `9` | |
|
`=1 xx (5 × 9 - 6 × 8) -2 xx (4 × 9 - 6 × 7) +3 xx (4 × 8 - 5 × 7)` `=1 xx (45 -48) -2 xx (36 -42) +3 xx (32 -35)` `=1 xx (-3) -2 xx (-6) +3 xx (-3)` `= -3 +12 -9` `=0` |
|
|
|
|
|
