Replacing 3x3 matrix with a value to work out the determinant

Question

Goodday,

I need some assistance with the following problem

Let

|a b c| |p q r| |x y z| = 6

and find

 det |a+x b+y c+z|
     |3x   3y  3z|
     |-p   -q  -r|  

My understanding is I can substitute the value 6 into the det below and then calculate the determinant.

I have done the calculation and it comes to 0.

I am not sure if I am on the right path here.

Thanks

Answer 1

Hint: what happens to a determinant when you interchange two rows, multiply a row by a constant, or add one row to another?

Answer 2

Hint: Determinant respects some row operations. Adding a multiple of a row to another row doesn't change the determinant. And if you multiply a row by $r$ then the determinant is multiplied by $r$ as well.