Home
Class 11
MATHS
Prove that |(1/a^(2),bc,b+c),(1/b^(2),ca...

Prove that `|(1/a^(2),bc,b+c),(1/b^(2),ca,c+a),(1/c^(2), ab, a+b)|=0`

Promotional Banner

Topper's Solved these Questions

  • SAMPLE PAPER - 3

    FULL MARKS|Exercise PART - IV|7 Videos

  • SAMPLE PAPER - 3

    FULL MARKS|Exercise PART-II|10 Videos

  • SAMPLE PAPER - 2

    FULL MARKS|Exercise PART - III|17 Videos

  • SAMPLE PAPER -17

    FULL MARKS|Exercise PART -IV|7 Videos

Similar Questions

Explore conceptually related problems

Prove that |(1,a,a^(2)-bc),(1,b,b^(2)-ca),(1,c,c^(2)-ab)|= 0 .

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)) ]:}

If a,b and c are non- zero real number then prove that |{:(b^(2)c^(2),,bc,,b+c),(c^(2)a^(2),,ca,,c+a),(a^(2)b^(2),,ab,,a+b):}| =0

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

Prove that {:[( a^(2) , bc, ac+c^(2)),( a^(2) +ab,b^(2) ,ac),( ab,b^(2) +bc,c^(2)) ]:} =4a^(2) b^(2) c^(2)

Prove that |(a^(2),bc,ac+c^(2)),(a^(2)+ab,b^(2),ac),(ab,b^(2)+bc,c^(2))|=4a^(2)b^(2)c^(2).

prove that |{:((b+c)^(2),,bc,,ac),(ba,,(c+a)^(2),,cb),(ca,,cb,,(a+b)^(2)):}| |{:((b+c)^(2),,a^(2),,a^(2)),(b^(2),,(c+a)^(2),,b^(2)),(c^(2),,c^(2),,(a+b)^(2)):}| =2abc (a+b+c)^(3)

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

Using properties of determinants, prove that |(-a^2,ab,ac),(ba,-b^2,bc),(ca,cb,-c^2)|=4a^2 b^2 c^2