If $\begin{vmatrix} a & b \\ c & d \end{vmatrix} = 4,$ then find
\[\begin{vmatrix} a & 7a + 3b \\ c & 7c  +3d \end{vmatrix}.\]
So, the determinant of the new matrix will be the same as the determinant of the old matrix The determinant of this matrix is $3-0=3$ So the determinant of the new matrix will be $4*3=12$ Yes, the determinant of the new matrix is $12$

