Let f be a linear transformation on plane m, then f 0 vector =0 vector.

Analytic f( 0) =(0 point 0 vector +0 point 0 vector) =0 point f( 0 vector) +0 point f(0 vector) =0 vector.

So once it's right,

Two pairs of vectors A belong to V. Let f(a vector) =2a vector, then f is a linear transformation on the plane m..

3. If E is the unit vector on the plane M, and for A belongs to V, let f(a)=a-e, then F is a linear transformation on the plane M..

F (λ a+μ b) = 2 (λ a+μ b) = λ (2a)+μ (2b) = λ f (a)+μ f (b), so the two are correct. For three, f (λ a+μ b) = (λ a+μ b)-e, λ f (a)+μ f (b) = λ (a-e)+μ (b-e) = λ a+μ b-(λ+μ)e, obviously (λ+μ) e and e.

Let F be a linear transformation on the plane M, and both A and B belong to V. If A and B are * * * lines, then f(a) and f(b) are also * * * lines.

For four, when A and B are * * * lines, if one of A and B is equal to 0 vector, because F (0) is equal to 0, that is, one of f(a) and f(b) is equal to 0 vector, and f(a) and F (b) are * * * lines; If a and b are not equal to zero vector, let b=λa, then there is a straight line F (b) = f (λ a+0+zero vector of zero point) = λ f(a)+zero point f(0)=λf(a), and then f (a) and F (b) b*** *.