What will happen to the following matrix if the third row is multiplied by 3?
3 3 3 1 5 6 3 4 5
Also, in general, how does scaling a row of a square matrix affect its determinant?
What will happen to the following matrix if the third row is multiplied by 3?
3 3 3 1 5 6 3 4 5
Also, in general, how does scaling a row of a square matrix affect its determinant?
The determinant is multiplied by the scaling factor. You can see this from the definition of the determinant as the signed sum of all products with one factor from each row and column – since each summand contains exactly one factor from the scaled row, each summand is scaled by the scaling factor, and thus so is the sum.
If you multiply a row by $n$, the determinant is multiplied by $n$.