waigaK

2020-12-07

Use the given coding matrices to encode and then decode the given message HELP.

$A=\left[\begin{array}{cc}4& -1\\ -3& 1\end{array}\right]$ and its inverse ${A}^{-1}=\left[\begin{array}{cc}1& 1\\ 3& 4\end{array}\right]$

insonsipthinye

Skilled2020-12-08Added 83 answers

Step 1

Concept:

A rectangular array of numbers (or other mathematical objects) for those the operations such as addition and multiplication are defined is called matrices. Matrix are used for plotting graph, statistics and also to do scientific studies and research in almost different fields.

Step 2

Given:

$A=\left[\begin{array}{cc}4& -1\\ -3& 1\end{array}\right]$ and its inverse

${A}^{-1}=\left[\begin{array}{cc}1& 1\\ 3& 4\end{array}\right]$

Step 3

Expressing the word numerically

The numerical equivalent of HELP is 8,5,12,16

Listing the numbers is the previous step by columns and form a square matrix

The$2\times 2$ matric formed by the numbers 8,5,12 and 16 is $\left[\begin{array}{cc}8& 12\\ 5& 16\end{array}\right]$

Step 4

Multiplying the matrix obtained by the given coding matrix A

$\left[\begin{array}{cc}4& -1\\ -3& 1\end{array}\right]\left[\begin{array}{cc}8& 12\\ 5& 16\end{array}\right]=\left[\begin{array}{cc}4(8)+(-1)(5)& 4(12)+(-1)(16)\\ (-3)(8)+1(5)& (-3)(12)+1(16)\end{array}\right]$

$=\left[\begin{array}{cc}27& 32\\ -19& -20\end{array}\right]$

Step 5

The encoded message is 27,-19,32,-20

The inverse is given as

${A}^{-1}=\left[\begin{array}{cc}1& 1\\ 3& 4\end{array}\right]$

$\left[\begin{array}{cc}1& 1\\ 3& 4\end{array}\right]\left[\begin{array}{cc}27& 32\\ -19& -20\end{array}\right]=\left[\begin{array}{cc}1(27)+1(-19)& 1(32)+1(-20)\\ 3(27)+4(-19)& 3(32)+4(-20)\end{array}\right]$

$=\left[\begin{array}{cc}8& 12\\ 5& 16\end{array}\right]$

Step 6

The numbers are 8,5,12 and 16

Therefore, the decoded message is HELP

Concept:

A rectangular array of numbers (or other mathematical objects) for those the operations such as addition and multiplication are defined is called matrices. Matrix are used for plotting graph, statistics and also to do scientific studies and research in almost different fields.

Step 2

Given:

Step 3

Expressing the word numerically

The numerical equivalent of HELP is 8,5,12,16

Listing the numbers is the previous step by columns and form a square matrix

The

Step 4

Multiplying the matrix obtained by the given coding matrix A

Step 5

The encoded message is 27,-19,32,-20

The inverse is given as

Step 6

The numbers are 8,5,12 and 16

Therefore, the decoded message is HELP

Jeffrey Jordon

Expert2022-01-23Added 2605 answers

Answer is given below (on video)

Jeffrey Jordon

Expert2022-08-23Added 2605 answers

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