Show that the given transformation from

R^(2)

to

R^(2)

is linear by showing that it is a matrix transformation.\

F

reflects a vector in the

y

-axis.\ Reflecting a vector in the

y

-axis means negating the

x

-coordinate. So\

F[[x],[y]]=[]=x[]+y[1]

\ and thus

F

is a matrix transformation with matrix\

F=[[|,|]].

\ It follows that

F

is a linear transformation.

Show that the given transformation from R2 to R2 is linear by showing that it is a matrix transformation. F reflects a vector in the y-axis. Reflecting a vector in the y-axis means negating the x-coordinate. So F[xy]=[]=x[]+y[], and thus F is a matrix transformation with matrix F=[]. It follows that F is a linear transformation