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Question Number 121523 by benjo_mathlover last updated on 09/Nov/20
$$\mathrm{Given}\:\mathrm{A}\:\mathrm{a}\:\mathrm{3x3}\:\mathrm{matrix}\:\mathrm{satisfy}\: \\ $$$$\rightarrow\begin{cases}{\mathrm{A}\begin{pmatrix}{\mathrm{1}}\\{\mathrm{2}}\\{\mathrm{3}}\end{pmatrix}\:=\:\begin{pmatrix}{\mathrm{3}}\\{\mathrm{4}}\\{\mathrm{2}}\end{pmatrix}}\\{\mathrm{A}\begin{pmatrix}{\mathrm{5}}\\{\mathrm{9}}\\{\mathrm{7}}\end{pmatrix}\:=\:\begin{pmatrix}{\mathrm{3}}\\{\mathrm{1}}\\{\mathrm{2}}\end{pmatrix}}\end{cases} \\ $$$$.\:\mathrm{Find}\:\mathrm{A}\begin{pmatrix}{\mathrm{10}}\\{\mathrm{18}}\\{\mathrm{14}}\end{pmatrix}\:?\: \\ $$
Commented by liberty last updated on 09/Nov/20
$$\Leftrightarrow\:\mathrm{A}\begin{pmatrix}{\mathrm{10}}\\{\mathrm{18}}\\{\mathrm{14}}\end{pmatrix}\:=\:\mathrm{2A}\begin{pmatrix}{\mathrm{5}}\\{\mathrm{9}}\\{\mathrm{7}}\end{pmatrix}\:=\:\mathrm{2}\begin{pmatrix}{\mathrm{3}}\\{\mathrm{1}}\\{\mathrm{2}}\end{pmatrix}\:=\:\begin{pmatrix}{\mathrm{6}}\\{\mathrm{2}}\\{\mathrm{4}}\end{pmatrix} \\ $$