InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
The value of the determinant `|(b +c,a -b,a),(c +a,b -c,b),(a +b,c -a,c)|`, isA. `a^(3) + b^(3) + c^(3) - 3abc`B. `3abc - a^(3) -b^(3) - c^(3)`C. `3 abc + a^(3) + b^(3) + c^(3)`D. none of these |
|
Answer» Correct Answer - B We have, `|(b +c,a -b,a),(c +a,b -c,b),(a +b,c -a,c)|` `= |(a +b +c,-b,a),(b +c +a,-c,b),(c +a +b,-a,c)| " " ["Applying " C_(1) rarr C_(1) + C_(3), C_(2) rarr -C_(2) - C_(3)]` `= - (a +b +c) |(1,b,a),(1,c,a),(1,a,c)|` `= -(a +b +c) |(1,b,a),(0,c -b,b -a),(0,a -b,c -a)| [(" Applying"),(R_(2) rarr R_(2) - R_(1) ", "R_(3) rarr R_(3) - R_(1))]` `= - (a + b +c) (a^(2) + b^(2) + c^(2)- ab - bc -ca)` `= - (a^(3) + b^(3) + c^(3) - 3abc)` |
|