Find the coefficient of x in the determinant `|((1+x)^(a_1 b_1),(1+x)^(a_1 b_2),(1+x)^(a_1 b_3)),((1+x)^(a_2 b_2),(1+x)^(a_2 b_2),(1+x)^(a_2 b_3)),((1+x)^(a_3 b_3),(1+x)^(a_3 b_2),(1+x)^(a_3 b_3))|=0.`

The value of the determinant (a_1-b_1)^2(a_1- b_2)^2(a_1-b_3)^2(a_1-b_4)^2(a_2-b_1)^2(a_2-b_2)^2(a_2-b_3)^2(a_2- b_4)^2(a_3-b_1)^2(a_3-b_2)^2(a_3-b_3)^2(a_3-b_4)^2(a_4-b_1)^2(a_4-b_2)^2(a_4-b_3)^2(a_4-b_4)^2 is dependant on a_i , i=1,2,3,4 dependant on b_i , i=1,2,3,4 dependant on a_(i j), b_i i=1,2,3,4

The value of the determinant |[a_1, la_1+mb_1, b_1],[a_2, la_2+mb_2, b_2],[a_3, la_3+mb_3, b_3]|=

Find the coordinates of the centroid of the triangle with its vertices at (a_1,b_1,c_1),(a_2,b_2,c_2), "and"(a_3, b_3,c_3).

The determinant |(b_1+c_1,c_1+a_1,a_1+b_1),(b_2+c_2,c_2+a_2,a_2+b_2),(b_3+c_3,c_3+a_3,a_3+b_3)|=

prove that |(1/(a-a_1)^2,1/(a-a_1),1/a_1),(1/(a-a_2)^2,1/(a-a_2),1/a_2),(1/(a-a_3)^2,1/(a-a_3),1/a_3)|=(-a^2(a_1-a_2)(a_2-a_3)(a_3-a_1))/(a_1a_2a_3(a-a_1)^2(a-a_2)^2(a-a_3)^2) .

If (a_2 a_3)/(a_1 a_4) = (a_2 + a_3)/(a_1 + a_4) = 3 ((a_2 - a_3)/(a_1 - a_4)) then a_1, a_2, a_3, a_4 are in

If the expression in powers of x of the function 1/((1-ax)(1-bx)) is a_0+a_1 x+a_2 x^2+a_3 x^3+... then a_n is

If a_1,a_2,a_3,a_4 are the coefficients of 2nd, 3rd, 4th and 5th terms of (1+x)^n respectively then (a_1)/(a_1+a_2) , (a_2)/(a_2+a_3),(a_3)/(a_3+a_4) are in