cochetezgh
2022-09-12
Answered

Find the slope of a line perpendicular to the line 3x−y=8

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Find the linear approximation of the function

Use L(x) to approximate the numbers

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What are two consecutive odd positive integers whose product is 323?

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Write the point slope form of the equation given (-6,-2) and m=3

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asked 2022-02-24

I already know how the set of solutions of system of linear equations over real numbers infinite field $PP$ is expressed.

When there is only single solution then it is just a vector of scalars, where each scalar is a real number.

When there are more than 1 solution, and actually infinite solutions, then it is just a parametric linear vector space in the form:$\mathrm{\forall}t\in \mathbb{R}:\overrightarrow{p}+\overrightarrow{v}\cdot t$ where $\overrightarrow{p}\in {\mathbb{R}}^{n}l{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\overrightarrow{v}\in {\mathbb{R}}^{n}$ where n denotes the number of real variables in each linear equation thus $n\in \mathbb{N}$

But my question is how the set of solutions of system of linear equations over the finite field$\mathbb{Z}}_{2$ or galois field GF(2) is expressed?

I already know that when there is only single solution then it is also just a vector of scalars, but where each scalar is a binary number either zero or one in$\mathbb{Z}}_{2$ where $\mathbb{Z}}_{2}=\{0,1\$ , but when there are more than 1 solution, but always finite number of solutions, then how are they expressed?

Is this similar to how real solutions are expressed by parametric linear vector space by modulo 2? Or something else? I don't know. I am trying to google the answer for this question for days but I don't find the answer anywhere. It seems like nobody talks about this topic.

How?

When there is only single solution then it is just a vector of scalars, where each scalar is a real number.

When there are more than 1 solution, and actually infinite solutions, then it is just a parametric linear vector space in the form:

But my question is how the set of solutions of system of linear equations over the finite field

I already know that when there is only single solution then it is also just a vector of scalars, but where each scalar is a binary number either zero or one in

Is this similar to how real solutions are expressed by parametric linear vector space by modulo 2? Or something else? I don't know. I am trying to google the answer for this question for days but I don't find the answer anywhere. It seems like nobody talks about this topic.

How?

asked 2021-02-01

Write the general forms of the equations of the lines that pass through the point and are (a) parallel to the given line and (b) perpendicular to the given line. Point (−1, 0) Line y=-3