" 18."|[a,a+2b,a+2b+3c],[3a,4a+6b,5a+7b+9c],[6a,9a+12b,11a+15b+18c]|=-a^(3)

If alpha=omega,b=omega^2,c=i , then the value of : |(a,a+2b,a+2b+3c),(3a,4a+6b,5a+7b+9c),(6a,9a+12b,11a+15b+18c)| is :

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

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

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

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

Let Delta=|(a,a+b,a+b+c),(3a,4a+3b,5a+4b+3c),(6a,9a+6b,11a+9b+6c)| where a=i, b=omega,c = omega^2 , then Delta is equal to

Suppose a,b,c epsilon R and Delta=|(a,a+b,a+b+c),(3a,4a+3b,5a+4b+3c),(6a,9a+6b,11a+9b+6c)| If Delta=11.728 then a=______