Question

Dina encoded a secret phrase using matrix multiplication. She multiplied the clear text code for each letter by the matrix (See image) to get a matrix that represents the encoded text. By which matrix does Dina multiply the encoded text to get the matrix for the clear text code?

Answer 1

C= 1 1

3 2

Explanation:

Answer 2

Dina needs to multiply by the inverse of C. The inverse of a 2×2 matrix is easily calculated from its definition: the transpose of the cofactor matrix divided by the determinant. Here, that is

`C^(-1)=\left[\begin{array}{cc}-1&-1\\-3&-2\end{array}\right] \cdot(1)/((-2)(-1)-(3)(1)) =\left[\begin{array}{cc}1&1\\3&2\end{array}\right]`