3-5-2-4-x-y-x-y-and-a-b-c-d-x-y-x-y-are-true-for-any-values-of-x-y-x-y-find-the-values-of-a-b-c-d-

Question Number 141152 by ZiYangLee last updated on 16/May/21

(\begin{matrix} 3 & 5 \\ 2 & 4 \end{matrix}) (\begin{matrix} x \\ y \end{matrix}) = (\begin{matrix} x^{'} \\ y^{'} \end{matrix}) and (\begin{matrix} a & b \\ c & d \end{matrix}) (\begin{matrix} x^{'} \\ y^{'} \end{matrix}) = (\begin{matrix} x \\ y \end{matrix})

are true for any values of x, y, x^{'}, y^{'},

find the values of a, b, c, d .

Answered by iloveisrael last updated on 16/May/21

\Rightarrow (\begin{matrix} 3 5 \\ 2 4 \end{matrix}) (\begin{matrix} a b \\ c d \end{matrix}) (\begin{matrix} x^{'} \\ y^{'} \end{matrix}) = (\begin{matrix} x^{'} \\ y^{'} \end{matrix})

\Rightarrow (\begin{matrix} a b \\ c d \end{matrix}) = {(\begin{matrix} 3 5 \\ 2 4 \end{matrix})}^{- 1} = \frac{1}{2} (\begin{matrix} 4 - 5 \\ - 2 3 \end{matrix})

= (\begin{matrix} 2 - 5 / 2 \\ - 1 3 / 2 \end{matrix})

Commented by ZiYangLee last updated on 16/May/21

Can i know how to get the first row ?

Commented by iloveisrael last updated on 16/May/21

b y s u b s t i t u t i o n

Answered by mr W last updated on 16/May/21

(\begin{matrix} 3 & 5 \\ 2 & 4 \end{matrix}) (\begin{matrix} x \\ y \end{matrix}) = (\begin{matrix} x^{'} \\ y^{'} \end{matrix}) a s g i v e n

\Rightarrow (\begin{matrix} x \\ y \end{matrix}) = {(\begin{matrix} 3 & 5 \\ 2 & 4 \end{matrix})}^{- 1} (\begin{matrix} x^{'} \\ y^{'} \end{matrix})

(\begin{matrix} x \\ y \end{matrix}) = (\begin{matrix} a & b \\ c & d \end{matrix}) (\begin{matrix} x^{'} \\ y^{'} \end{matrix}) a s g i v e n

\Rightarrow (\begin{matrix} a & b \\ c & d \end{matrix}) = {(\begin{matrix} 3 & 5 \\ 2 & 4 \end{matrix})}^{- 1} = (\begin{matrix} 2 & - 2.5 \\ - 1 & 1.5 \end{matrix})

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