सिक्ष कीजिए `|[a,a+b,a+b+c],[2a,3a+2b,4a+3b+2c],[3a,6a+3b,10a+6b+3c]|=a^(3)`

Show that: |aa+ba+b+c2a3a+2b4a+3b+2c3a6a+3b10a+6b+3c|=a^(3)

Using properties of determinants,prove that det[[a,a+b,a+b+c2a,3a+2b,4a+3b+2c3a,6a+3b,10a+6b+3c]]=a^(3)

Prove that |a a+b a+b+c2a3a+2B4a+3b+2c3a6a+3b 10 a+6b+3c|=a^3

If a=omega!=1 , is a cube root of unity b=785,c=2008i and Delta=|(a,a+b,a+b+c),(2a,3a+2b,4a+3b+2c),(3a,6a+3b,10a+6b+3c)| then Delta equals

|[a, a+2b, a+2b+3c], [3a, 4a+6b, 5a+7b+9c], [6a, 9a+12b, 11a+15b+18c]|=?

Add: 3a - 4b + 4c, 2a + 3b - 8c, a - 6b + c

2a - 3b - [3a - 2b - {a - c- (a - 2b)}]

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 ?

Add: 6a + 8b - 5c, 2b + c - 4a and a - 3b - 2c.