f is a linear transformation
At least one of the answers above is NOT correct.
(1 point) Let $f: R^2 \rightarrow R$ be defined by $f((x, y)) = 6x - 7y$. Is $f$ a linear transformation?
a. $f((x_1, y_1) + (x_2, y_2)) = 6x_1 + 6x_2 - 7y_1 - 7y_2$
$f((x_1, y_1)) + f((x_2, y_2)) = 6x_1 - 7y_1 + 6x_2 - 7y_2$
Does $f((x_1, y_1) + (x_2, y_2)) = f((x_1, y_1)) + f((x_2, y_2))$ for all $(x_1, y_1), (x_2, y_2) \in R^2$? Yes, they are equal
b. $f(c(x, y)) = 6cx - 7cy$
$cf((x, y)) = c(6x - 7y)$
Does $f(c(x, y)) = cf((x, y))$ for all $c \in R$ and all $(x, y) \in R^2$? Yes, they are equal
c. Is $f$ a linear transformation? f is a linear transformation
Note: In order to get credit for this problem all answers must be correct.
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