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Question-164133




Question Number 164133 by Avijit007 last updated on 14/Jan/22
Answered by cortano1 last updated on 15/Jan/22
 A= [((a    b)),((c    d)) ]; B= [((e    f)),((g    h)) ]    [((2a+3e    2b+3f)),((2c+3g     2d+3h)) ]=  [((8     3)),((7     6)) ]    [((a+e    b+g)),((c+f    d+h)) ]=  [((3      1)),((3      3)) ]   2a+3e=8            2d+3h=6   2a+2e=6            2d+2h=6    e=2 ; a=1          h=0 , d=3   { ((2b+3f=3)),((2c+3g=7)) :}     { ((b+g=1)),((c+f=3)) :}
$$\:{A}=\begin{bmatrix}{{a}\:\:\:\:{b}}\\{{c}\:\:\:\:{d}}\end{bmatrix};\:{B}=\begin{bmatrix}{{e}\:\:\:\:{f}}\\{{g}\:\:\:\:{h}}\end{bmatrix} \\ $$$$\:\begin{bmatrix}{\mathrm{2}{a}+\mathrm{3}{e}\:\:\:\:\mathrm{2}{b}+\mathrm{3}{f}}\\{\mathrm{2}{c}+\mathrm{3}{g}\:\:\:\:\:\mathrm{2}{d}+\mathrm{3}{h}}\end{bmatrix}=\:\begin{bmatrix}{\mathrm{8}\:\:\:\:\:\mathrm{3}}\\{\mathrm{7}\:\:\:\:\:\mathrm{6}}\end{bmatrix} \\ $$$$\:\begin{bmatrix}{{a}+{e}\:\:\:\:{b}+{g}}\\{{c}+{f}\:\:\:\:{d}+{h}}\end{bmatrix}=\:\begin{bmatrix}{\mathrm{3}\:\:\:\:\:\:\mathrm{1}}\\{\mathrm{3}\:\:\:\:\:\:\mathrm{3}}\end{bmatrix} \\ $$$$\:\mathrm{2}{a}+\mathrm{3}{e}=\mathrm{8}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}{d}+\mathrm{3}{h}=\mathrm{6} \\ $$$$\:\mathrm{2}{a}+\mathrm{2}{e}=\mathrm{6}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}{d}+\mathrm{2}{h}=\mathrm{6} \\ $$$$\:\:{e}=\mathrm{2}\:;\:{a}=\mathrm{1}\:\:\:\:\:\:\:\:\:\:{h}=\mathrm{0}\:,\:{d}=\mathrm{3} \\ $$$$\begin{cases}{\mathrm{2}{b}+\mathrm{3}{f}=\mathrm{3}}\\{\mathrm{2}{c}+\mathrm{3}{g}=\mathrm{7}}\end{cases}\:\:\:\:\begin{cases}{{b}+{g}=\mathrm{1}}\\{{c}+{f}=\mathrm{3}}\end{cases} \\ $$

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