Question

−5
3
2
​
⋅(−1
2
1
​
)

Answer 1

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 \( C \):

1. For \( C_{11} \):
\[
C_{11} = (-5)(-1) + (3)(1) = 5 + 3 = 8
\]

2. For \( C_{12} \):
\[
C_{12} = (-5)(2) + (3)(1) = -10 + 3 = -7
\]

3. For \( C_{21} \):
\[
C_{21} = (2)(-1) + (1)(1) = -2 + 1 = -1
\]

4. 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!