Home
Class 12
MATHS
By using properties of determinants , s...

By using properties of determinants , show that : (i) ` {:[( 1,a,a^(2)),( 1,b,b^(2)),( 1,c,c^(2))]:}=(a-b)(b-c) (c-a) `
(ii) ` {:[( 1,1,1),( a,b,c) ,(a^(3) , b^(3), c^(3))]:} =( a-b) (b-c)( c-a) (a+b+c) `

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    NCERT TAMIL|Exercise EXERCISE 4.3|7 Videos
  • DETERMINANTS

    NCERT TAMIL|Exercise EXERCISE 4.4|5 Videos
  • DETERMINANTS

    NCERT TAMIL|Exercise EXERCISE 4.1|8 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    NCERT TAMIL|Exercise MISCELLANEOUS EXERCISE ON CHAPTER 5|23 Videos
  • DIFFERENTIAL EQUATIONS

    NCERT TAMIL|Exercise MISCELLANEOUS EXERCISE|18 Videos

Similar Questions

Explore conceptually related problems

Prove that |(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2))|=(a-b)(b-c)(c-a)

Prove that |{:(1,a,a^2),(1,b,b^2),(1,c,c^2):}|=(a-b)(b-c)(c-a) .

Show that |(b+c,a,a^(2)),(c+a,b,b^(2)),(a+b,c,c^(2))|=(a+b+c)(a-b)(b-c)(c-a)

By using properties of determinants , show that : {:[( a^(2) + 1, ab,ac),(ab,b^(2) + 1,bc),( ca, cb, c^(2) +1) ]:}= 1+a^(2) +b^(2) +c^(2)

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

Using properties of determinants Prove that |{:(a+b+c,,-c,,-b),(-c,,a+b+c,,-a),( -b,,-a,,a+b+c):}| = 2 (a+b) (b+c) (c+a)

Prove that |{:(a,,a^(2),,bc),(b ,,b^(2),,ac),( c,,c^(2),,ab):}| |{:(1,,1,,1),(a^(2) ,,b^(2),,c^(2)),( a^(3),, b^(3),,c^(3)):}|

Without expanding the determinant, prove that {:[( a, a ^(2), bc ),( b ,b ^(2) , ca),( c, c ^(2) , ab ) ]:} ={:[( 1, a^(2) , a^(3) ),( 1,b^(2) , b^(3) ),( 1, c^(2),c^(3)) ]:}

Prove that Delta = |{:(1,,1,,1),(a,,b,,c),(bc+1^(2),,ac+b^(2),,ab+c^(2)):}| = 2(a-b)(b-c)(c-1)

Using the property of determinants and without expanding {:[( a-b,b-c, c-a),( b-c,c-a,a-b),( c-a,a-b,b-c)]:} =0