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Question Number 110948 by bemath last updated on 01/Sep/20

$$\sqrt{\mathrm{bemath}}$$$$\mathrm{If}\mathrm{each}\mathrm{point}\mathrm{on}\mathrm{the}\mathrm{line}3\mathrm{x}+4\mathrm{y}=2$$$$\mathrm{is}\mathrm{transformed}\mathrm{by}\mathrm{matrix}\mathrm{M}=\left(\begin{array}{c}20\\ 01\end{array}\right),\mathrm{the}$$$$\mathrm{image}\mathrm{is}\mathrm{a}\mathrm{line}\mathrm{\_}\mathrm{\_}\mathrm{\_}$$

Commented by bemath last updated on 01/Sep/20

$$\mathrm{hshahaha}....\mathrm{bemath}\mathrm{sir}.\mathrm{bemath}\mathrm{macho}$$

Commented by Rasheed.Sindhi last updated on 01/Sep/20

$$\mathcal{T}hankyoumydear!$$

Commented by bobhans last updated on 01/Sep/20

$$\mathrm{standart}\mathrm{way}$$$$\left(\begin{array}{c}{\mathrm{x}}^{\prime }\\ {\mathrm{y}}^{\prime }\end{array}\right)=\left(\begin{array}{c}20\\ 01\end{array}\right)\left(\begin{array}{c}\mathrm{x}\\ \mathrm{y}\end{array}\right)\Rightarrow \left(\begin{array}{c}\mathrm{x}\\ \mathrm{y}\end{array}\right)=\frac{1}{2}\left(\begin{array}{c}10\\ 02\end{array}\right)\left(\begin{array}{c}{\mathrm{x}}^{\prime }\\ {\mathrm{y}}^{\prime }\end{array}\right)$$$$\left(\begin{array}{c}\mathrm{x}\\ \mathrm{y}\end{array}\right)=\frac{1}{2}\left(\begin{array}{c}{\mathrm{x}}^{\prime }\\ {2\mathrm{y}}^{\prime }\end{array}\right)=\left(\begin{array}{c}\frac{1}{2}{\mathrm{x}}^{\prime }\\ {\mathrm{y}}^{\prime }\end{array}\right)$$$$\mathrm{hence}\mathrm{the}\mathrm{image}\mathrm{of}\mathrm{line}\mathrm{is}\frac{3}{2}{\mathrm{x}}^{\prime }+{4\mathrm{y}}^{\prime }=2$$$$\mathrm{multiply}\mathrm{by}2\Rightarrow 3\mathrm{x}+8\mathrm{y}-4=0$$

Commented by Rasheed.Sindhi last updated on 01/Sep/20

$$\sqrt{\mathrm{bemath}}=\sqrt{\mathrm{b}}\sqrt{\mathrm{e}}\sqrt{\mathrm{m}}\sqrt{\mathrm{a}}\sqrt{\mathrm{t}}\sqrt{\mathrm{h}}:)$$

Commented by bemath last updated on 01/Sep/20

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Commented by Rasheed.Sindhi last updated on 01/Sep/20

$$\mathrm{BTW},be-mathorbem-ath$$$$orsomethingelse?$$

Answered by bobhans last updated on 01/Sep/20

$$\mathrm{say}\mathrm{the}\mathrm{image}\mathrm{is}\mathrm{a}\mathrm{line}\ell \equiv \mathrm{x}\left|\begin{array}{c}34\\ 01\end{array}\right|+\mathrm{y}\left|\begin{array}{c}20\\ 34\end{array}\right|-2.\left|\begin{array}{c}20\\ 01\end{array}\right|=0$$$$\ell \equiv 3\mathrm{x}+8\mathrm{y}-4=0$$

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