Question

Determine whether L:R^2 -- R^3, L (​

Answer 1

Answer:

function T:Rn→Rm is called a linear transformation if T satisfies the following two linearity conditions: For any x,y∈Rn and c∈R, we have

T(x+y)=T(x)+T(y)

T(cx)=cT(x)

The nullspace N(T) of a linear transformation T:Rn→Rm is

N(T)={x∈Rn∣T(x)=0m}.

The nullity of T is the dimension of N(T).

The range R(T) of a linear transformation T:Rn→Rm is

R(T)={y∈Rm∣y=T(x) for some x∈Rn}.

The rank of T is the dimension of R(T).

The matrix representation of a linear transformation T:Rn→Rm is an m×n matrix A such that T(x)=Ax for all x∈Rn.