The file you uploaded contains an extra credit problem related to cryptography using linear algebra, specifically Hill's cipher. The problem involves a few tasks:

(a) Compute $K^{-1}$, the inverse of the matrix $K$.

To compute the inverse of the key matrix $K$, we use the formula for the inverse of a 3x3 matrix, which is: $K^{-1} = \frac{1}{\text{det}(K)} \cdot \text{adj}(K)$ Where:

• $\text{det}(K)$ is the determinant of the matrix.
• $\text{adj}(K)$ is the adjugate (or adjoint) of the matrix.

The matrix $K$ is given by:

1 & 2 & -2 \\ 2 & 3 & 0 \\ 1 & 1 & 1 \end{pmatrix}$$ I'll proceed with calculating the inverse. Let's first find the determinant and the adjugate of $$K$$. ### (b) Decrypt the encrypted sequence. You're also asked to decrypt the sequence of numbers: $$\{-23, -8, 5, -3, 22, 18, -11, -28, -13\}$$ This sequence has been encrypted using the matrix $$K$$, and using the inverse $$K^{-1}$$, we can recover the original sequence and interpret it as text. Would you like me to continue with the detailed calculations for both tasks?