$\begin{array}{rl}\mathrm{ln}(x)& =3\mathrm{ln}(y)\\ \text{}{3}^{x}& ={27}^{y}\end{array}$

kolutastmr
2022-07-02
Answered

Logarithmic system of equations

$\begin{array}{rl}\mathrm{ln}(x)& =3\mathrm{ln}(y)\\ \text{}{3}^{x}& ={27}^{y}\end{array}$

$\begin{array}{rl}\mathrm{ln}(x)& =3\mathrm{ln}(y)\\ \text{}{3}^{x}& ={27}^{y}\end{array}$

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asked 2022-07-02

Let $A$ and $B$ be two $2\times 2$-matrices, and considering the equation

$AX=B$

Where $X$ is an unknown $2\times 2$-matrix. What I want to do is explain why the equation is equivalent to solving two $2\times 2$-systems of equations simultaneously and determine how this generalizes to $n\times n$.

And, on the corollary, let $A,B,C$ be three $2\times 2$-matrices and consider the equation

$AX+XB=C$

What I want to do here explain why you can not solve this as two $2\times 2$-systems of equations simultaneously

$AX=B$

Where $X$ is an unknown $2\times 2$-matrix. What I want to do is explain why the equation is equivalent to solving two $2\times 2$-systems of equations simultaneously and determine how this generalizes to $n\times n$.

And, on the corollary, let $A,B,C$ be three $2\times 2$-matrices and consider the equation

$AX+XB=C$

What I want to do here explain why you can not solve this as two $2\times 2$-systems of equations simultaneously

asked 2022-07-02

Solve a set of non linear Equations on Galois Field

${M}_{1}=\frac{{y}_{1}-{y}_{0}}{{x}_{1}-{x}_{0}}$

${M}_{2}=\frac{{y}_{2}-{y}_{0}}{{x}_{2}-{x}_{0}}$

${M}_{1},{M}_{2},{x}_{1},{y}_{1},{x}_{2},{y}_{2},$, are known and they are chosen from a $GF({2}^{m}).$. I want to find ${x}_{0},{y}_{0}$I ll restate my question. Someone chose three distinct ${x}_{0},{x}_{1},{x}_{2}$, as well as ${y}_{0},{y}_{1},{y}_{2}$, then computed ${M}_{1},{M}_{2}$, and finally revealed ${M}_{1},{M}_{2},{x}_{1},{y}_{1},{x}_{2},{y}_{2}$, but not ${x}_{0},{y}_{0}.$ to us.All the variables are chosen from a Galois Field.

I want to recover the unknown ${x}_{0},{y}_{0}.$. Is it possible to accomplish that?

If a set of nonlinear equations have been constructed with the aforementioned procedure e.g.

${M}_{1}=\frac{{k}_{1}-({y}_{0}+(\frac{{y}_{1}-{y}_{0}}{{x}_{1}-{x}_{0}})({l}_{1}-{x}_{0}))}{({l}_{1}-{x}_{0})({l}_{1}-{x}_{1})}$

${M}_{2}=\frac{{k}_{2}-({y}_{0}+(\frac{{y}_{1}-{y}_{0}}{{x}_{1}-{x}_{0}})({l}_{2}-{x}_{0}))}{({l}_{2}-{x}_{0})({l}_{2}-{x}_{1})}$

${M}_{3}=\frac{{k}_{3}-({y}_{0}+(\frac{{y}_{1}-{y}_{0}}{{x}_{1}-{x}_{0}})({l}_{3}-{x}_{0}))}{({l}_{3}-{x}_{0})({l}_{3}-{x}_{1})}$

${M}_{4}=\frac{{k}_{4}-({y}_{0}+(\frac{{y}_{1}-{y}_{0}}{{x}_{1}-{x}_{0}})({l}_{4}-{x}_{0}))}{({l}_{4}-{x}_{0})({l}_{4}-{x}_{1})}$

where ${x}_{0},{y}_{0}{x}_{1},{y}_{1}$ are the unknown GF elements. Can I recover the unknown elements?

My question was if the fact that the set of equations is defined on a Galois Field imposes any difficulties to find its solution.

If not I suppose that the set can be solved. Is this true?

${M}_{1}=\frac{{y}_{1}-{y}_{0}}{{x}_{1}-{x}_{0}}$

${M}_{2}=\frac{{y}_{2}-{y}_{0}}{{x}_{2}-{x}_{0}}$

${M}_{1},{M}_{2},{x}_{1},{y}_{1},{x}_{2},{y}_{2},$, are known and they are chosen from a $GF({2}^{m}).$. I want to find ${x}_{0},{y}_{0}$I ll restate my question. Someone chose three distinct ${x}_{0},{x}_{1},{x}_{2}$, as well as ${y}_{0},{y}_{1},{y}_{2}$, then computed ${M}_{1},{M}_{2}$, and finally revealed ${M}_{1},{M}_{2},{x}_{1},{y}_{1},{x}_{2},{y}_{2}$, but not ${x}_{0},{y}_{0}.$ to us.All the variables are chosen from a Galois Field.

I want to recover the unknown ${x}_{0},{y}_{0}.$. Is it possible to accomplish that?

If a set of nonlinear equations have been constructed with the aforementioned procedure e.g.

${M}_{1}=\frac{{k}_{1}-({y}_{0}+(\frac{{y}_{1}-{y}_{0}}{{x}_{1}-{x}_{0}})({l}_{1}-{x}_{0}))}{({l}_{1}-{x}_{0})({l}_{1}-{x}_{1})}$

${M}_{2}=\frac{{k}_{2}-({y}_{0}+(\frac{{y}_{1}-{y}_{0}}{{x}_{1}-{x}_{0}})({l}_{2}-{x}_{0}))}{({l}_{2}-{x}_{0})({l}_{2}-{x}_{1})}$

${M}_{3}=\frac{{k}_{3}-({y}_{0}+(\frac{{y}_{1}-{y}_{0}}{{x}_{1}-{x}_{0}})({l}_{3}-{x}_{0}))}{({l}_{3}-{x}_{0})({l}_{3}-{x}_{1})}$

${M}_{4}=\frac{{k}_{4}-({y}_{0}+(\frac{{y}_{1}-{y}_{0}}{{x}_{1}-{x}_{0}})({l}_{4}-{x}_{0}))}{({l}_{4}-{x}_{0})({l}_{4}-{x}_{1})}$

where ${x}_{0},{y}_{0}{x}_{1},{y}_{1}$ are the unknown GF elements. Can I recover the unknown elements?

My question was if the fact that the set of equations is defined on a Galois Field imposes any difficulties to find its solution.

If not I suppose that the set can be solved. Is this true?

asked 2021-06-16

Solve the system by clennaton

The solution is ( . )

asked 2022-09-07

Equations:

$$\{\begin{array}{l}K=\frac{B\u20133}{20}\\ K=(20S+3)R+S\\ K=20{S}^{2}+(20N+7)S+N\\ N=R-S\end{array}$$

$B$ values, e.g: $$834343,\text{}3253538,\text{}{10}^{87653}$$

How to find the $R$ values?

$$\{\begin{array}{l}K=\frac{B\u20133}{20}\\ K=(20S+3)R+S\\ K=20{S}^{2}+(20N+7)S+N\\ N=R-S\end{array}$$

$B$ values, e.g: $$834343,\text{}3253538,\text{}{10}^{87653}$$

How to find the $R$ values?

asked 2020-11-08

4x−6y=12

−2x+3y=−6

−2x+3y=−6

asked 2022-09-01

Write Octave statements to solve the following linear system. You don't have to find the final values for x, y, and z.

$6x-4y+z=3\phantom{\rule{0ex}{0ex}}3y-7=-4\phantom{\rule{0ex}{0ex}}x+9y-5z=5$

$6x-4y+z=3\phantom{\rule{0ex}{0ex}}3y-7=-4\phantom{\rule{0ex}{0ex}}x+9y-5z=5$

asked 2021-09-09

Consider the system of equations described by

1. Write down the system of equations in matrix form.

2. Find the eigenvalues of the system of equations.

3. Find the associated eigenvectors.