1. **Problem Statement:** Given two matrices $ A = \begin{bmatrix} 2 & x \\ 3 & 4 \end{bmatrix} $ and $ B = \begin{bmatrix} y & 5 \\ 3 & z \end{bmatrix} $, find the values of $ x $, $ y $, and $ z $ such that $ A = B $. 2. **Formula and Rules:** Two matrices are equal if and only if their corresponding elements are equal. That means: $$ A_{ij} = B_{ij} \quad \text{for all } i,j $$ 3. **Set up equations from equality:** From the matrices, equate each element: - Top-left: $ 2 = y $ - Top-right: $ x = 5 $ - Bottom-left: $ 3 = 3 $ (already equal) - Bottom-right: $ 4 = z $ 4. **Solve for unknowns:** - From $ 2 = y $, we get $ y = 2 $ - From $ x = 5 $, we get $ x = 5 $ - From $ 4 = z $, we get $ z = 4 $ 5. **Final answer:** $$ x = 5, \quad y = 2, \quad z = 4 $$ This means the matrices are equal when these values are substituted.