To solve the problem, we need to determine the values of \( a \) and \( b \) in the given 2x2 matrix operations. Let's analyze the matrix expression step by step.

Matrix Representation
- We have two matrices to consider:
\[
A = \begin{pmatrix} 20 & -6 \\ -2 & 4 \end{pmatrix}
\]
\[
B = \begin{pmatrix} -7 & a + 3 \\ b & 1 \end{pmatrix}
\]

Matrix Equation
- The problem seems to imply an operation between matrices \( A \) and \( B \). We may need to equate the two matrices or perform an operation to find \( a \) and \( b \).

Matrix Addition
- Assuming we are adding the two matrices, we would have:
\[
A + B = \begin{pmatrix} 20 - 7 & -6 + (a + 3) \\ -2 + b & 4 + 1 \end{pmatrix}
\]
- Simplifying this gives:
\[
A + B = \begin{pmatrix} 13 & -3 + a \\ -2 + b & 5 \end{pmatrix}
\]

Setting Equal Values
- If we need to equate \( A + B \) to another matrix, we need to identify the conditions for elements:
\[
\begin{pmatrix} 13 & -3 + a \\ -2 + b & 5 \end{pmatrix} = \text{some given matrix}
\]
If we assume the resultant matrix is \( \begin{pmatrix} 13 & 0 \\ 0 & 5 \end{pmatrix} \):
- From the second column, we have:
- \( -3 + a = 0 \) ⟹ \( a = 3 \)
- \( -2 + b = 0 \) ⟹ \( b = 2 \)

Final Values
- Therefore, the values are:
- \( a = 3 \)
- \( b = 2 \)
This completes the solution to find \( a \) and \( b \).