Home
Class 12
MATHS
Express Deltaas a product to two detemin...

Express `Delta`as a product to two deteminants and then find its value.
`Delta=|{:((a-x)^2,(b-x)^2,(c-x)^2),((a-y)^2,(b-y)^2,(c-y)^2),((a-z)^2,(b-z)^2,(c-z)^2):}|`

Text Solution

AI Generated Solution

To solve the problem, we need to express the determinant \( \Delta \) as a product of two determinants and then find its value. Given: \[ \Delta = \begin{vmatrix} (a-x)^2 & (b-x)^2 & (c-x)^2 \\ (a-y)^2 & (b-y)^2 & (c-y)^2 \\ (a-z)^2 & (b-z)^2 & (c-z)^2 ...
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    AAKASH INSTITUTE|Exercise Try Yourself|12 Videos
  • DETERMINANTS

    AAKASH INSTITUTE|Exercise SECTION A|33 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    AAKASH INSTITUTE|Exercise section - J|6 Videos
  • DIFFERENTIAL EQUATIONS

    AAKASH INSTITUTE|Exercise Assignment Section - J (Aakash Challengers Questions)|4 Videos

Similar Questions

Explore conceptually related problems

Without expanding, show that "Delta"=|(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y)^2(b-z)^2(c-x)^2(c-y)^2(c-z)^2|=2(a-b)(b-c)(c-a)(x-y)(y-z)(z-x)

Prove that the value of each the following determinants is zero: (a^(x)+a^(-x))^(2),(a^(x)-a^(-x))^(2),1(b^(y)+b^(-y))^(2),(b^(y)-+b^(-y))^(2),1(c^(z)+c^(-z))^(2),(c^(z)-c^(-z))^(2),1]|

If a, b,c> 0 and x,y,z in R then the determinant: |((a^x+a^-x)^2,(a^x-a^-x)^2,1),((b^y+b^-y)^2,(b^y-b^-y)^2,1),((c^z+c^-z)^2,(c^z-c^-z)^2,1)| is equal to

The value of Delta = |((a^(x) + a^(-x))^(2),(a^(x) -a^(-x))^(2),1),((a^(y) + a^(-y))^(2),(a^(y) -a^(-y))^(2),1),((a^(z) + a^(-z))^(2),(a^(z) - a^(-z))^(2),1)| , is

If a,b,c>0 and x,y,z in R then |[(a^x+a^(-x))^2, (a^x-a^(-x))^2, 1] , [(b^y+b^(-y))^2, (b^y-b^(-y))^2, 1], [(c^z+c^(-z))^2, (c^z-c^(-z))^2, 1]|=

det[[1,x,x^(2)1,y,y^(2)1,z,z^(2)]]det[[a^(2),1,2ab^(2),1,2b1,z,z^(2)]]det[[a^(2),1,2ab^(2),1,2bc^(2),1,2c]]=det[[(a-x)^(2),(b-x^(2)),(c-x)^(2)(a-y)^(2),(b-y)^(2),(c-y)^(2)(a-z)^(2),(b-z)^(2),(c-z)^(2)]]

prove that |{:((a-x)^(2),,(a-y)^(2),,(a-z)^(2)),((b-x)^(2),,(b-y)^(2),,(b-z)^(2)),((c-x)^(2),,(c-y)^(2),,(c-z)^(2)):}| |{:((1+ax)^(2),,(1+bx)^(2),,(1+cx)^(2)),((1+ay)^(2),,(1+by)^(2),,(1+cy)^(2)),((1+az)^(2),,(1+bx)^(2),,(1+cz)^(2)):}| =2 (b-c)(c-a)(a-b)xx (y-z) (z-x)(x-y)

If Delta=|{:(,x,2y-z,-z),(,y,2x-z,-z),(,y,2y-z,2x-2y-z):}| ,then

If x=asecthetacostheta,y=bsecthetasinthetaandz=thetatantheta , then find the value of (x^(2))/(a^(2))+(y^(2))/(b^(2))-(z^(2))/(c^(2))