# Write the uncoded row matrices for the message. Message: SELL CONSOLIDATED Row Matrix Size: 1 times 3 Encoding Matrix: A=begin{bmatrix}1 & -1&0 1 & 0&

Write the uncoded row matrices for the message.
Message: SELL CONSOLIDATED
Row Matrix Size: $1×3$
Encoding Matrix: $A=\left[\begin{array}{ccc}1& -1& 0\\ 1& 0& -1\\ -6& 3& 2\end{array}\right]$
SEL=$\left[\begin{array}{ccc}19& 5& 12\end{array}\right]$
L-C=$\left[\begin{array}{ccc}12& 0& 3\end{array}\right]$
ONS=$\left[\begin{array}{ccc}15& 14& 19\end{array}\right]$
OLI=$\left[\begin{array}{ccc}15& 12& 9\end{array}\right]$
DAT=$\left[\begin{array}{ccc}4& 1& 20\end{array}\right]$
ED=$\left[\begin{array}{ccc}5& 4& 0\end{array}\right]$
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Step 1
Given
the given message is "SELL CONSOLIDATED".
Encoding matrix $A=\left[\begin{array}{ccc}1& -1& 0\\ 1& 0& -1\\ -6& 3& 2\end{array}\right]$
Step 2
Calculation
Generate $1×3$ uncoded row matrices for the given message.
SEL=$\left[\begin{array}{ccc}19& 5& 12\end{array}\right]$
L-C=$\left[\begin{array}{ccc}12& 0& 3\end{array}\right]$
ONS=$\left[\begin{array}{ccc}15& 14& 19\end{array}\right]$
OLI=$\left[\begin{array}{ccc}15& 12& 9\end{array}\right]$
DAT=$\left[\begin{array}{ccc}4& 1& 20\end{array}\right]$
ED=$\left[\begin{array}{ccc}5& 4& 0\end{array}\right]$
For the coded matrices, multiply each uncoded row matrix by A.
$\left[\begin{array}{ccc}19& 5& 12\end{array}\right]\left[\begin{array}{ccc}1& -1& 0\\ 1& 0& -1\\ -6& 3& 2\end{array}\right]$
$=\left[\begin{array}{ccc}19×1+5×1+12×\left(-6\right)& 19×\left(-1\right)+5×0+12×3& 19×0+5×\left(-1\right)+12×2\end{array}\right]$
$=\left[\begin{array}{ccc}-48& 17& 19\end{array}\right]$
$\left[\begin{array}{ccc}12& 0& 3\end{array}\right]\left[\begin{array}{ccc}1& -1& 0\\ 1& 0& -1\\ -6& 3& 2\end{array}\right]$
$=\left[\begin{array}{ccc}12×1+0×1+3×\left(-6\right)& 12×\left(-1\right)+0×0+3×3& 12×0+0×\left(-1\right)+3×2\end{array}\right]$
$=\left[\begin{array}{ccc}-6& -3& 6\end{array}\right]$
$\left[\begin{array}{ccc}15& 14& 19\end{array}\right]\left[\begin{array}{ccc}1& -1& 0\\ 1& 0& -1\\ -6& 3& 2\end{array}\right]$
$=\left[\begin{array}{ccc}15×1+14×1+19×\left(-6\right)& 15×\left(-1\right)+14×0+19×3& 15×0+14×\left(-1\right)+19×2\end{array}\right]$
$=\left[\begin{array}{ccc}-85& 42& 24\end{array}\right]$
$\left[\begin{array}{ccc}15& 12& 9\end{array}\right]\left[\begin{array}{ccc}1& -1& 0\\ 1& 0& -1\\ -6& 3& 2\end{array}\right]$
$=\left[\begin{array}{ccc}15×1+12×1+9×\left(-6\right)& 15×\left(-1\right)+12×0+9×3& 15×0+12×\left(-1\right)+9×2\end{array}\right]$
$=\left[\begin{array}{ccc}-27& 12& 6\end{array}\right]$
$\left[\begin{array}{ccc}4& 1& 20\end{array}\right]\left[\begin{array}{ccc}1& -1& 0\\ 1& 0& -1\\ -6& 3& 2\end{array}\right]$
$=\left[\begin{array}{ccc}4×1+1×1+20×\left(-6\right)& 4×\left(-1\right)+1×0+20×3& 4×0+1×\left(-1\right)+20×2\end{array}\right]$
$=\left[\begin{array}{ccc}-115& 56& 39\end{array}\right]$
Jeffrey Jordon