[hline a+b,2a+b,3a+b,],[hline2a+b,3a+b,4a+b,=0],[hline4a+b,5a+b,6a+b,]

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]|

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

Without expanding the determinant, prove that |{:(a+b, 2a+b, 3a+b),(2a+b, 3a+b, 4a+b), (4a+b, 5a+b, 6a+b):}|=0.

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]]

Consider abs[[a,a+b,a+b+c],[2a,3a+2b,4a+3b+2c],[3a,6a+3b,10a+6b+3c]]

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+b,a+2b,a+3b] , [a+3b,a+4b,a+5b] , [a+5b,a+6b,a+7b]|=0

Without expanding show that following : |[a,a+b,a+b+c],[2a,3a+2b,4a+3b+2c],[3a,6a+3b,10a+6b+3c]| = a^3