([a+b,2a+b,3a+b],[2a+b,3a+b,4a+b],[4a+b,5a+b,6a+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 following : |[a,a+b,a+b+c],[2a,3a+2b,4a+3b+2c],[3a,6a+3b,10a+6b+3c]| = a^3

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

Show that: |[a, a+b ,a+b+c],[2a,3a+2b,4a+3b+2c],[3a,6a+3b, 10 a+6b+3c]|=a^3 .

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

Without expanding the following determinant, show that : |[3a+b, 2a, a],[4a+3b, 3a, 3a],[5a+6b,4a,6a]|=a^3

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|

Select and write the correct answer from the given alternatives in each of the following: |(a+b,a+2b,a+3b),(a+2b,a+3b,a+4b),(a+4b,a+5b,a+6b)| =