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E-is-reported-in-i-j-base-e-1-2i-3j-e-2-i-2j-and-e-3-4i-5j-belong-to-E-1-Determinate-the-cordonnates-of-e-3-in-the-base-B-e-1-e-2-




Question Number 88756 by mathocean1 last updated on 12/Apr/20
E is reported in (i^→ ;j^→ ) base.  e_1 ^→ =2i^→ +3j^→  ;   e_2 ^→ =i^→ −2j^→  and   e_3 ^→ =4i^→ −5j^→    belong to E.  1)Determinate the cordonnates of e_3 ^→  in the   base B(e_1 ^→ ;e_2 ^→ ).
$$\mathrm{E}\:\mathrm{is}\:\mathrm{reported}\:\mathrm{in}\:\left(\overset{\rightarrow} {\mathrm{i}};\overset{\rightarrow} {\mathrm{j}}\right)\:\mathrm{base}. \\ $$$$\overset{\rightarrow} {\mathrm{e}}_{\mathrm{1}} =\mathrm{2}\overset{\rightarrow} {\mathrm{i}}+\mathrm{3}\overset{\rightarrow} {\mathrm{j}}\:;\:\:\:\overset{\rightarrow} {\mathrm{e}}_{\mathrm{2}} =\overset{\rightarrow} {\mathrm{i}}−\mathrm{2}\overset{\rightarrow} {\mathrm{j}}\:\mathrm{and}\:\:\:\overset{\rightarrow} {\mathrm{e}}_{\mathrm{3}} =\mathrm{4}\overset{\rightarrow} {\mathrm{i}}−\mathrm{5}\overset{\rightarrow} {\mathrm{j}}\: \\ $$$$\mathrm{belong}\:\mathrm{to}\:\mathrm{E}. \\ $$$$\left.\mathrm{1}\right)\mathrm{Determinate}\:\mathrm{the}\:\mathrm{cordonnates}\:\mathrm{of}\:\overset{\rightarrow} {\mathrm{e}}_{\mathrm{3}} \:\mathrm{in}\:\mathrm{the}\: \\ $$$$\mathrm{base}\:\mathrm{B}\left(\overset{\rightarrow} {\mathrm{e}}_{\mathrm{1}} ;\overset{\rightarrow} {\mathrm{e}}_{\mathrm{2}} \right). \\ $$

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