Without expanding, show that the value of each of the determinants is zero: `|a+b2a+b3a+b2a+b3a+b4a+b4a+b5a+b6a+b|`

Explanation

Take, ` triangle= |[a+b,2a+b, 3a+b],[2a+b,3a+b,4a+b],[4a+b,5a+b,6a+b]|`

using `c_3 rightarrow c_3 - c_2` we have

` triangle= |[a+b,2a+b, a],[2a+b,3a+b,a],[4a+b,5a+b,a]|`

using `c_2 rightarrow c_2 - c_1` we get

` triangle= |[a+b,a, a],[2a+b,a,a],[4a+b,a,a]|`

then, `c_2 =c_3`

hence determinant is zero