Home
Class 12
MATHS
Using the property of determinants and w...

Using the property of determinants and without expanding, prove that:`|0a-b-a0-c b c0|=0`

Text Solution

Verified by Experts

`Let Delta=|{:(0,a,-b),(-a,0,-c),(b,c,0):}|=0`
`rArr" " Delta=(-1)(-1)(-1)|{:(0,a,-b),(-a,0,-c),(b,c,0):}|=0`
`rArr" " Delta=-|{:(0,a,-b),(-a,0,-c),(b,c,0):}|=0" "(CharrR)`
`rArr" "Delta=-Delta`
`rArr" "2Delta=0rArr" "Delta=0` Hence Proved.
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    NAGEEN PRAKASHAN|Exercise Exercise 4.3|5 Videos

  • DETERMINANTS

    NAGEEN PRAKASHAN|Exercise Exercise 4.4|5 Videos

  • DETERMINANTS

    NAGEEN PRAKASHAN|Exercise Exercise 4.1|8 Videos

  • Continuity and Differentiability

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|23 Videos

  • DIFFERENTIAL EQUATIONS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|18 Videos

Similar Questions

Explore conceptually related problems

Prove that: |0a-b-a0-cbc0|=0

Using the property of determinants and without expanding,prove that: det[[0,a,-b-a,0,-cb,c,0]]=0

Using the property of determinants and without expanding,prove that: det[[a-b,b-c,c-ab-c,c-a,a-bc-a,a-b,b-c]]=0

Using the property of determinants and without expanding,prove that: det[[-a^(2),ab,acba,b^(2),bcca,cb,-c^(2)]]=4a^(2)b^(2)c^(2)

Using the property of determinants and without expanding,prove that: det[[1,bc,a(b+c)1,ca,b(c+a)1,ab,x(a+b)]]=0

Using the property of determinants and without expanding prove that abs([1,1,1],[a,b,c],[a^3,b^3,c^3])=(a-b)(b-c)(c-a)(a+b+c)

Using the property of determinants and without expanding,prove that: det[[x,a,x+ay,b,y+bz,c,z+c]]=0

Using the property of determinants and without expanding, prove that |(2,7,65), (3,8,75), (5,9,86)|=0

Using the property of determinants and without expanding in questions 1 to 7 prove that , |{:(x,a,x+a),(y,b,y+b),(z,c,z+c):}|=0

Using the property of determinants and without expanding in questions 1 to 7 prove that , |{:(a-b,b-c,c-a),(b-c,c-a,a-b),(c-a,a-b,b-c):}|=0