Resolução do exercício de GAAL

nao sei

a)

A transformação será:

\[\eqalign{ & T{\text{ }}\left( {1,0} \right){\text{ }} = {\text{ }}\left( {2,1} \right){\text{ }} \cr & T{\text{ }}\left( {0,1} \right){\text{ }} = {\text{ }}\left( {1,4} \right) \cr & \cr & T\left( {x,y} \right) = \alpha \left( {{x_1},{y_1}} \right) + \beta \left( {{x_2},{y_2}} \right) \cr & T\left( {x,y} \right) = \alpha \left( {2,1} \right) + \beta \left( {1,4} \right) \cr & T\left( {x,y} \right) = 2\alpha + \alpha + \beta + 4\beta \cr & T\left( {x,y} \right) = 3\alpha + 5\beta }\]

b)

\[\eqalign{ & T\left( {x,y} \right) = 3\alpha + 5\beta \cr & T{\text{ }}\left( {2,3} \right) = 3 \cdot 2 + 5 \cdot 3 \cr & T{\text{ }}\left( {2,3} \right) = 6 + 15 \cr & T{\text{ }}\left( {2,3} \right) = 21{\text{ }} }\]