It appears that you're trying to perform a matrix multiplication with two matrices. However, the way the matrices are presented is a little unclear due to the formatting.
Assuming you mean the following matrices:
\[ A = \begin{pmatrix} -5 & 3 \ 2 & 1 \end{pmatrix} \]
and
\[ B = \begin{pmatrix} -1 & 2 \ 1 & 1 \end{pmatrix} \]
To multiply these two matrices \( A \) and \( B \), you can use the matrix multiplication formula. The element \( (i,j) \) in the resulting matrix \( C = A \cdot B \) is calculated as follows:
\[ C_{ij} = \sum_{k} A_{ik} B_{kj} \]
Calculating the elements of \( C \):
-
For \( C_{11} \): \[ C_{11} = (-5)(-1) + (3)(1) = 5 + 3 = 8 \]
-
For \( C_{12} \): \[ C_{12} = (-5)(2) + (3)(1) = -10 + 3 = -7 \]
-
For \( C_{21} \): \[ C_{21} = (2)(-1) + (1)(1) = -2 + 1 = -1 \]
-
For \( C_{22} \): \[ C_{22} = (2)(2) + (1)(1) = 4 + 1 = 5 \]
Thus, the resulting matrix \( C \) is:
\[ C = \begin{pmatrix} 8 & -7 \ -1 & 5 \end{pmatrix} \]
If my assumption about the matrices is incorrect or if you're looking for something else, please clarify!