Calvin encoded a secret phrase using matrix multiplication. Using A = 1, B = 2, C = 3, and so on, he multiplied the clear text c
ode for each letter by the matrix c=3 -2 4 -3 to get a matrix that represents the encoded text. The matrix representing the encoded text is...... What is the secret phrase? Determine the location of spaces after you decode the text.
Our matrix C is the encoder. Let X be our secret message and let B be our encoded message. Therefore the relationship between the 3 can be represented as:
CX = B
So we want to solve for X (our secret message). So using matrix algebra:
X = C^-1*B where C^-1 is the inverse of C.
C^-1 = | 3 -2 | |4 -3 |
So we take C^-1 and multiply it by matrix B to get X. Matrix B is already given to us. So just multiply those two. I used a calculator to get:
