|
26. determinants using properties of determinants example
( Enter your problem )
|
- Example `[[201,210,220],[151,155,140],[50,55,80]]`
- Example `[[100,205,105],[200,408,207],[300,608,310]]`
- Example `[[2,1970,1978],[5,1960,1980],[7,1950,1978]]`
- Example `[[1977,1979,1981],[1940,1943,1946],[10,17,24]]`
|
|
3. Example `[[2,1970,1978],[5,1960,1980],[7,1950,1978]]`
Find value of determinant using properties of determinants ...
`[[2,1970,1978],[5,1960,1980],[7,1950,1978]]`Solution:| `A=` | | 2 | 1970 | 1978 | | | 5 | 1960 | 1980 | | | 7 | 1950 | 1978 | |
|
Now, `C_3=C_3 - C_2` | `=` | | 2 | 1970 | 8 | | | 5 | 1960 | 20 | | | 7 | 1950 | 28 | |
|
take 4 as a comman factor from `C_3` | `=4 xx ` | | 2 | 1970 | 2 | | | 5 | 1960 | 5 | | | 7 | 1950 | 7 | |
|
Here `C_1=C_3`, So value of the determinant is 0 `=4 xx 0` `=0` Method-2: Determinant by expanding cofactors| `|A|` | = | | `2` | `1970` | `1978` | | | `5` | `1960` | `1980` | | | `7` | `1950` | `1978` | |
|
| = | | | `2` | | × | | | `1960` | `1980` | | | `1950` | `1978` | |
|
| | |
`=2 xx (1960 × 1978 - 1980 × 1950) -1970 xx (5 × 1978 - 1980 × 7) +1978 xx (5 × 1950 - 1960 × 7)` `=2 xx (3876880 -3861000) -1970 xx (9890 -13860) +1978 xx (9750 -13720)` `=2 xx (15880) -1970 xx (-3970) +1978 xx (-3970)` `= 31760 +7820900 -7852660` `=0`
This material is intended as a summary. Use your textbook for detail explanation.Any bug, improvement, feedback then Submit Here
|
|
|
