The matrix C=[1,-2_-3,7] was used to encode a phrase to [7,-28,-25,-35,-2_-21,107,90,123,17]. Find C^-1 and use it to decode the matrix.

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16-12-2016
Mathematics

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The matrix C=[1,-2_-3,7] was used to encode a phrase to [7,-28,-25,-35,-2_-21,107,90,123,17]. Find C^-1 and use it to decode the matrix.

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nobillionaireNobley nobillionaireNobley · Answer 1 · 2016-12-23T02:36:40-05:00

\(C= \left[\begin{array}{cc}1&-2\\-3&7\end{array}\right] \\ C^{-1}= \left[\begin{array}{cc}7&2\\3&1\end{array}\right] \\ \left[\begin{array}{cc}7&2\\3&1\end{array}\right] \times \left[\begin{array}{ccccc}7&-28&-25&-35&-2\\-21&107&90&123&17\end{array}\right] \\ =\left[\begin{array}{ccccc}49-42&-196+214&-175+180&-245+246&-14+34\\21-21&-84+107&-75+90&-105+123&-6+17\end{array}\right] \\ =\left[\begin{array}{ccccc}7&18&5&1&20\\0&23&15&18&11\end{array}\right]\)
is the required matrix.