Determine a transformação linear T:R 3 →R 2 �:�3→�2  tal que T(1,0,0)=(2,0) �(1,0,0)=(2,0) , T(0,1,0)=(1,1) �(0,1,0)=(1,1)  e T(0,0,1)=(0,−1) �(0,0...

Determine a transformação linear T:R

3

→R

2

�:�3→�2

 tal que T(1,0,0)=(2,0)

�(1,0,0)=(2,0)

, T(0,1,0)=(1,1)

�(0,1,0)=(1,1)

 e T(0,0,1)=(0,−1)

�(0,0,1)=(0,−1)

.

a.

T(x,y,z)=(x−2y,2y+z)

�(�,�,�)=(�−2�,2�+�)

.

b.

T(x,y,z)=(2x+y,y−z)

�(�,�,�)=(2�+�,�−�)

.

c.

T(x,y,z)=(x+y,y+z)

�(�,�,�)=(�+�,�+�)

.

d.

T(x,y,z)=(x+2y,3y−z)

�(�,�,�)=(�+2�,3�−�)

.

e.

T(x,y,z)=(2x−y,y−3z)

�(�,�,�)=(2�−�,�−3�)

.