Let f : R<sup>2</sup> → R be defined by f((x, y)) = 7x + 3y. Is f a linear transformation?
a. f((x<sub>1</sub>, y<sub>1</sub>) + (x<sub>2</sub>, y<sub>2</sub>)) =
f((x<sub>1</sub>, y<sub>1</sub>)) + f((x<sub>2</sub>, y<sub>2</sub>)) =
Does f((x<sub>1</sub>, y<sub>1</sub>) + (x<sub>2</sub>, y<sub>2</sub>)) = f((x<sub>1</sub>, y<sub>1</sub>)) + f((x<sub>2</sub>, y<sub>2</sub>)) for all (x<sub>1</sub>, y<sub>1</sub>), (x<sub>2</sub>, y<sub>2</sub>) ∈ R<sup>2</sup>?
b. f(c(x, y)) =
c(f((x, y))) =
Does f(c(x, y)) = c(f((x, y))) for all c ∈ R and all (x, y) ∈ R<sup>2</sup>?
c. Is f a linear transformation?