`|{:(a+b,2a+b,3a+b),(2a+b,3a+b,4a+b),(4a+b,5a+b,6a+b):}|=0`

Which of the following has value not equal to zero ? a) |(8,2,7),(12,3,5),(16,4,3)| b) |(1//a,a^(2),bc),(1//b,b^(2),ac),(1//c,c^(2),ab)| c) |(a+b,2a+b,3a+b),(2a+b,3a+b,4a+b),(4a+b,5a+b,6a+b)| d) |(2,43,6),(7,35,4),(3,17,2)|

Prove that |{:(a,a+b,a=b+c),(2a,3a+2b,4a+3b+2c),(3a,6a+3b,10a+6b+3c):}|=a^3

Evaluate : |{:(a,a+b,a+b+c),(2a,3a+2b,4a+3b+2c),(3a,6a+3b,10a+6b+3c):}|

Which of the following has/have value equal to zero? |[8, 2, 7],[ 12, 3, 5],[ 16, 4, 3]| b. |[1//a, a^2,b c],[1//b,b^2,a c],[1//c,c^2,a b]| c. |[a+b,2a+b,3a+b],[2a+b,3a+b,4a+b],[4a+b,5a+b,6a+b]| d. |[2, 43, 3],[ 7, 35, 4],[ 3, 17, 2]|

Using properties of determinants, prove that: |{:(a, a +b, a+b+c),(2a, 3a + 2b, 4a + 3b + 2c),(3a, 6a+3b, 10a + 6b + 3c):}| = a^(3)

Prove that |(a,a+b,a+b+c),(2a,3a+2b,4a+3b+2c),(3a,6a+3b,10a+6b+3c)| = a^(3)

Prove that |(a,a+b, a+b+c),(2a,3a+2b,4a+3b+2c),(3a,6a+3b,10a,6b+3c)| = a^3

The determinant |{:(a+b+c,a+b,a),(4a+3b+2c,3a+2b,2a),(10a+6b+3c,6a+3b,3a):}| is independent of which one of the following ?