Describe in words the region of R^{3} represented by the equation(s) or inequality. x = 5

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asked 2020-11-14

Consider the bases \(\displaystyle{B}={\left({b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{c}\right\rbrace}{b}{e}{g}\in{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{2}\backslash{3}{e}{n}{d}{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace},{b}{e}{g}\in{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{3}\backslash{5}{e}{n}{d}{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\right)}{o}{f}{R}^{{2}}{\quad\text{and}\quad}{C}={\left({b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{c}\right\rbrace}{b}{e}{g}\in{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{1}\backslash{1}\backslash{0}{e}{n}{d}{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace},{b}{e}{g}\in{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{1}\backslash{0}\backslash{1}{e}{n}{d}{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace},{b}{e}{g}\in{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{0}\backslash{1}\backslash{1}{e}{n}{d}{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}\right)}{o}{f}{R}^{{3}}\).
and the linear maps PSKS \in L (R^2, R^3) and T \in L(R^3, R^2) given given (with respect to the standard bases) by \(\displaystyle{\left[{S}\right]}_{{{E},{E}}}={b}{e}{g}\in{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{2}&-{1}\backslash{5}&-{3}\backslash-{3}&{2}{e}{n}{d}{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{\quad\text{and}\quad}{\left[{T}\right]}_{{{E},{E}}}={b}{e}{g}\in{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{1}&-{1}&{1}\backslash{1}&{1}&-{1}{e}{n}{d}{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}\) Find each of the following coordinate representations. \(\displaystyle{\left({b}\right)}{\left[{S}\right]}_{{{E},{C}}}\)
\(\displaystyle{\left({c}\right)}{\left[{S}\right]}_{{{B},{C}}}\)

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asked 2021-02-25

Consider the bases \(\displaystyle{B}={\left({b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{c}\right\rbrace}{b}{e}{g}\in{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{2}\backslash{3}{e}{n}{d}{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace},{b}{e}{g}\in{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{3}\backslash{5}{e}{n}{d}{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\right)}{o}{f}{R}^{{2}}{\quad\text{and}\quad}{C}={\left({b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{c}\right\rbrace}{b}{e}{g}\in{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{1}\backslash{1}\backslash{0}{e}{n}{d}{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace},{b}{e}{g}\in{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{1}\backslash{0}\backslash{1}{e}{n}{d}{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace},{b}{e}{g}\in{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{0}\backslash{1}\backslash{1}{e}{n}{d}{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}\right)}{o}{f}{R}^{{3}}\).
and the linear maps PSKS \in L (R^2, R^3) and T \in L(R^3, R^2) given given (with respect to the standard bases) by \(\displaystyle{\left[{S}\right]}_{{{E},{E}}}={b}{e}{g}\in{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{2}&-{1}\backslash{5}&-{3}\backslash-{3}&{2}{e}{n}{d}{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{\quad\text{and}\quad}{\left[{T}\right]}_{{{E},{E}}}={b}{e}{g}\in{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{1}&-{1}&{1}\backslash{1}&{1}&-{1}{e}{n}{d}{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}\) Find each of the following coordinate representations. \(\displaystyle{\left({a}\right)}{\left[{S}\right]}_{{{B},{E}}}\)

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asked 2020-12-14

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asked 2021-02-27

The system of equation \(\displaystyle{d}{i}{s}{p}{l}{a}{y}{s}{t}{y}\le{\left\lbrace{b}\right\rbrace}{\left\lbrace{e}\right\rbrace}{\left\lbrace{g}\right\rbrace}\in{\left\lbrace\le{f}{t}{\left\lbrace{\left\lbrace{c}\right\rbrace}{\left\lbrace{a}\right\rbrace}{\left\lbrace{s}\right\rbrace}{\left\lbrace{e}\right\rbrace}{\left\lbrace{s}\right\rbrace}{r}{i}{g}{h}{t}\right\rbrace}\right\rbrace}{\frac{{{n}}}{{{\left\lbrace{2}\right\rbrace}}}}\backslash-{\frac{{{\left\lbrace{\left\lbrace{n}\right\rbrace}+{\left\lbrace{1}\right\rbrace}\right\rbrace}}}{{{\left\lbrace{2}\right\rbrace}}}}{\left\lbrace{e}\right\rbrace}{\left\lbrace{n}\right\rbrace}{\left\lbrace{d}\right\rbrace}{\left\lbrace\le{f}{t}{\left\lbrace{\left\lbrace{c}\right\rbrace}{\left\lbrace{a}\right\rbrace}{\left\lbrace{s}\right\rbrace}{\left\lbrace{e}\right\rbrace}{\left\lbrace{s}\right\rbrace}{r}{i}{g}{h}{t}\right\rbrace}\right\rbrace}\) by graphing method and if the system has no solution then the solution is inconsistent.
Given: The linear equations is \(\displaystyle{d}{i}{s}{p}{l}{a}{y}{s}{t}{y}\le{\left\lbrace{2}\right\rbrace}{\left\lbrace{x}\right\rbrace}+{\left\lbrace{y}\right\rbrace}={\left\lbrace{1}\right\rbrace}{\left\lbrace\quad\text{and}\quad\right\rbrace}{\left\lbrace{4}\right\rbrace}{\left\lbrace{x}\right\rbrace}+{\left\lbrace{2}\right\rbrace}{\left\lbrace{y}\right\rbrace}={\left\lbrace{3}\right\rbrace}.\)

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asked 2020-12-24

To write: The inequalites to describe the region of a solid cylinder that lies on or below the plane \(\displaystyle{z}={8}\) and on or above the disk in the xy - plane with the center at origin and radius 2.

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asked 2021-01-30

A line L through the origin in \(\displaystyle\mathbb{R}^{{3}}\) can be represented by parametric equations of the form x = at, y = bt, and z = ct. Use these equations to show that L is a subspase of \(\displaystyle\mathbb{R}^{{3}}{b}{y}{s}{h}{o}{w}\in{g}{t}\hat{{\quad\text{if}\quad}}{v}_{{1}}={\left({x}_{{1}},{y}_{{1}},{z}_{{1}}\right)}{\quad\text{and}\quad}{v}_{{2}}={\left({x}_{{2}},{y}_{{2}},{z}_{{2}}\right)}{a}{r}{e}{p}\oint{s}{o}{n}{L}{\quad\text{and}\quad}{k}{i}{s}{a}{n}{y}{r}{e}{a}{l}\nu{m}{b}{e}{r},{t}{h}{e}{n}{k}{v}_{{1}}{\quad\text{and}\quad}{v}_{{1}}+{v}_{{2}}\) are also points on L.

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Answer 1

1) Concept:
The equation of the plane parallel to yz- plane is \(x = a\)
2) Given:
\(x = 5\)
3) Calculation:
The given equation is \(x = 5\)
The equation \(x = 5\) represents the set of all points in \(R^{3}\) whose x coordinate is 5.
That is \({(x, y, z) |\ x = 5, y \in R, z \in R}\)
This is a plane which is parellel to yz plane and five units in front of it.
Therefore,
\(x = 5\)
represents a plane in \(R^{3}\) parallel to yz plane and five units in front of it.
Conclusion:
\(x = 5\)
represents a plane in \(R^{3}\) parallel to yz plane and five units in front of it.

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Describe in words the region of R^{3} represented by the equation(s) or inequality. x = 5

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