Find-the-image-of-y-3x-1-under-the-mapping-2-3-1-2-

Question Number 57805 by pete last updated on 12/Apr/19

Find the image of y = 3 x + 1 under the

mapping (\begin{matrix} 2 3 \\ 1 2 \end{matrix}) .

Commented by pete last updated on 12/Apr/19

thanks very much sir

Commented by mr W last updated on 12/Apr/19

p o i n t 1 (0, 1)

\Rightarrow i m a g e (3, 2)

p o i n t 2 (- \frac{1}{3}, 0)

\Rightarrow i m a g e (- \frac{2}{3}, - \frac{1}{3})

e q n . o f i m a g e :

\frac{y + \frac{1}{3}}{x + \frac{2}{3}} = \frac{2 + \frac{1}{3}}{3 + \frac{2}{3}}

\frac{3 y + 1}{3 x + 2} = \frac{7}{11}

\Rightarrow 11 y = 7 x + 1

Answered by mr W last updated on 13/Apr/19

l e t i m a g e o f p o i n t (x, y) b e (u, v),

(\begin{matrix} u \\ v \end{matrix}) = (\begin{matrix} 2 & 3 \\ 1 & 2 \end{matrix}) (\begin{matrix} x \\ y \end{matrix})

\Rightarrow (\begin{matrix} x \\ y \end{matrix}) = (\begin{matrix} 2 & - 3 \\ - 1 & 2 \end{matrix}) (\begin{matrix} u \\ v \end{matrix})

\Rightarrow x = 2 u - 3 v

\Rightarrow y = - u + 2 v

\Rightarrow - u + 2 v = 3 (2 u - 3 v) + 1

\Rightarrow 11 v = 7 u + 1

i . e . i m a g e i s 11 y = 7 x + 1

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