SamverkanLinalgLIU

2. Bestäm matrisen till den linjära avbildningen \displaystyle F:{\bf R^3}\rightarrow{\bf R}^3 som i basen \displaystyle \underline{\boldsymbol{e}}=\{\boldsymbol{e}_1, \boldsymbol{e}_2,\boldsymbol{e}_3\} definieras genom

\displaystyle F(\boldsymbol{e}_1+\boldsymbol{e}_2)=2\boldsymbol{e}_1+\boldsymbol{e}_2,\qquad F(\boldsymbol{e}_2+\boldsymbol{e}_3)=-\boldsymbol{e}_1+2\boldsymbol{e}_2+\boldsymbol{e}_3,\qquad F(\boldsymbol{e}_1)=2\boldsymbol{e}_1+\boldsymbol{e}_2+5\boldsymbol{e}_3.

Svar \displaystyle \begin{pmatrix}0&2&-3\\0&1&1\\-5&5&-4\end{pmatrix}