Question

Which of the following is/are true ?

• A. Every linear transformation from $\R^2$ to $\R^2$ maps lines onto points or lines
• B. Every surjective linear transformation from $\R^2$ to $\R^2$ maps lines onto lines
• C. Every bijective linear transformation from $\R^2$ to $\R^2$ maps pairs of parallel lines to pairs of parallel lines
• D. Every bijective linear transformation from $\R^2$ to $\R^2$ maps pairs of perpendicular lines to pairs of perpendicular lines

Answer 1

Answer: (A), (B), (C)

Every linear transformation from $\R^2$ to $\R^2$ maps lines onto points or lines

Answer 2

The correct option is (A) : Every linear transformation from $\R^2$ to $\R^2$ maps lines onto points or lines, (B) : Every surjective linear transformation from $\R^2$ to $\R^2$ maps lines onto lines and (C) : Every bijective linear transformation from $\R^2$ to $\R^2$ maps pairs of parallel lines to pairs of parallel lines.