Without expanding, show that the value of each of the determinants is zero: `|1/a a^2b c a/bb^2a c a/cc^2a b|`

Without expanding, show that the value of each of the determinants is zero: |1/a a^2 bc 1/b b^2 ac 1/c c^2 ab|

Without expanding, show that the value of each of the following determinants is zero: |1//a , a^2b c1//bb^2a c1//cc^2a b| (ii) |a+b2a+b3a+b2a+b3a+b4a+b4a+b5a+b6a+b| (iii) |1a a^2 1bb^2 1cc^2\ \ \ -b c-a c-a b|

Without expanding, show that the value of each of the determinants is zero: |[1,a, a^2-bc],[1,b,b^2-ac],[1,c,c^2-ab]|

Without expanding, show that the value of each of the determinants is zero: |[1,a, a^2-bc],[1,b,b^2-ac],[1,c,c^2-ab]|

Without expanding, show that the value of each of the determinants is zero: |a+b2a+b3a+b2a+b3a+b4a+b4a+b5a+b6a+b|

Without expanding,show that the value of each of the determinants is zero: det[[a+b,2a+b,3a+b2a+b,3a+b,4a+b4a+b,5a+b,6a+b]]

Without expanding, show that the value of the following determinant is zero: |[49, 1, 6], [39, 7, 4], [26, 2, 3]|

Prove that: |1a a^2-b c1bb^2-c a1cc^2-a b|=0

Prove that: |1a a^2-b c1bb^2-c a1cc^2-a b|=0

Without expanding,show that the values of the following determinants are zero: |(a,b,c),(2,5,7),(a+4,b+10,c+14)|