Solve for x : `|(x+a,b,c),(a,x+b,c),(a,b,x+c)|=0`

Prove that |(a,b,c),(a-b,b-c,c-a),(b+c,c+a,a+b)| = a^(3) + b^(3) + c^(3) - 3abc .

Prove that |(3a, -a+b, -a+c),(a-b, 3b, c-b),(a-c, b-c, 3c)| = 3(a+b+c)(ab+bc+ca) .

Solve: a(x-a) = b(x-b)

Without expanding show that : |(a+b,b+c,c+a),(b+c,c+a,a+b),(c+a,a+b,b+c)|=2|(a,b,c),(b,c,a),(c,a,b)|

If a,b,c are in A.P., show that : |(x+1,x+2,x+a),(x+2,x+3,x+b),(x+3,x+4,x+c)|=0

Solve: a(x+b) = 2ax + b

Which of the followings are relations from {x, y, z} to {a, b, c, d} {(a, x),(b,y), (c, z)}

What is the value of following determinant ? |(a-b, b-c, c-a),(b-c, c-a, a-b),(c-a, a-b, b-c)|

Find the value of : |(b+c,a,a),(b,c+a,b),(c,c,a+b)|

Which of the followings are relations from {x, y, z} to {a, b, c, d} {(x, a),(x, b),(x, c), (x, d),(y, a) (y, b),(y, c),(y, d)}