Step 1: Calculate the determinant of the given matrix. The determinant of a $2 \times 2$ matrix $\begin{bmatrix} a & b \\ c & d \end{bmatrix}$ is given by $ad - bc$. For the given matrix $\begin{bmatrix} y-1 & 2 \\ 4 & 3 \end{bmatrix}$, the determinant is: $$ (y-1)(3) - (2)(4) $$ Step 2: Set the determinant equal to $4$ as given in the problem. $$ 3(y-1) - 8 = 4 $$ Step 3: Expand and simplify the equation. $$ 3y - 3 - 8 = 4 $$ $$ 3y - 11 = 4 $$ Step 4: Solve for $y$. Add $11$ to both sides of the equation: $$ 3y = 4 + 11 $$ $$ 3y = 15 $$ Divide by $3$: $$ y = \frac{15}{3} $$ $$ y = 5 $$ The value of $y$ is: $$ \boxed{5} $$ Send me the next one 📸