If `A_1B_1C_1 , A_2B_2C_2 and A_3B_3C_3` are three digit numbers, each of which is divisible by k, then `Delta = |(A_1,B_1,C_1),(A_2,B_2,C_2),(A_3,B_3,C_3)|` is divisible by ____

If a_1b_1c_1,a_2b_2c_2 and a_3b_3c_3 are three digit even natural numbers and Delta =|[c_1,a_1,b_1],[c_2,a_2,b_2],[c_3,a_3,b_3]| ,t h e n Delta i s divisible by 2 but not necessarily by 4 divisible by 4 but not necessarily by 8 divisible by 8 none of these

If x_i=a_i b_i c_i,i=1,2,3 are three-digit positive integer such that each x_1 is a multiple of 19, then for some integers n , prove that |[a_1,a_2,a_3],[b_1,b_2,b_3],[c_1,c_2,c_3]| is divisible by 19.

For three distinct positive numbers a, b, c with a + b + c = 1, show that 8abc le (2/3)^3 .

If A_1,B_1,C_1, are respectively, the cofactors of the elements a_1, b_1,c_1, of the determinant "Delta"=|[a_1b_1c_1][a_2b_2c_2][a_3b_3c_3]|,"Delta"!=0 , then the value of |[B_2C_2][B_3C_3]| is equal to a. a1^2Δ b. a_1Δ c. a_1^2Δ d. a1 2^2Δ

Prove that the value of each the following determinants is zero: |[a_1,l a_1+mb_1,b_1],[a_2,l a_2+mb_2,b_2],[a_3,l a_3+m b_3,b_3]|

Delta = |(a, a^2, 0),(1, 2a+b,(a+b)),(0, 1, 2a+3b)| is divisible by a. a+b b. a+2b c. 2a+3b d. a^2

Find the coordinates of the centriod of the triangle whose vertices are ( a_(1), b_(1), c_(1)) , (a_(2), b_(2), c_(2)) and (a_(3), b_(3), c_(3)) .

The area of the triangle whose vertices are A(1,-1,2),B(2,1-1)C(3,-1,2) is …….

If |x_1y_1 1x_2y_2 1x_3y_3 1|=|a_1b_1 1a_2b_2 1a_3b_3 1| then the two triangles with vertices (x_1, y_1),(x_2,y_2),(x_3,y_3) and (a_1,b_1),(a_2,b_2),(a_3,b_3) are equal to area (b) similar congruent (d) none of these

If Delta=|(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)| and Delta_1=|(a_1+pb_1,b_1+qc_1,c_1+ra_1),(a_2+pb_2,b_2+qc_2,c _2+ra_2),(a_3+pb_3,b_3+qc_3,c_3+ra_3)| then Delta_1=