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

Answer:

C= 1   1

    3  2

Step-by-step 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

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