Find b

Given:

\[ \begin{bmatrix} a – b & 2a + c \\ 2a – b & 3c + d \end{bmatrix} = \begin{bmatrix} -1 & 5 \\ 0 & 13 \end{bmatrix} \]

Step 1: Form Equations

\[ a – b = -1 \quad (1) \]

\[ 2a – b = 0 \quad (2) \]

Step 2: Subtract (1) from (2)

\[ (2a – b) – (a – b) = 0 – (-1) \]

\[ a = 1 \]

Step 3: Substitute into (2)

\[ 2(1) – b = 0 \Rightarrow b = 2 \]

Final Answer:

\[ \boxed{b = 2} \]