Question

Which of the following function t:r2-r2 is not a linear transformation

Answer 1

Answer:

= r(t, s,1 + t + s) = rT(v) and so T does not preserve scalar multiplication: hence it is not a linear transformation. ... Find the matrix corresponding to the linear transformation T : R2 → R3 given by T(x1, x2)=(x1 −x2, x1 + x2, x1).

Answer 2

Answer:

The function T:R2→R3T:R2→R3 is a not a linear transformation.

Step-by-step explanation:

• A linear transformation is a function from one vector space to another that respects the underlying (linear) structure of each vector space
• A linear transformation is transformation T:Rn→Rm satisfying

T(u+v)=T(u)+T(v)

T(cu)=cT(u)

for all vectors u,v in Rn and all scalars c.

Let T:Rn→Rm be a matrix transformation: T(x)=Ax for an m×n matrix A. By this proposition in Section 2.3, we have

T(u+v)=A(u+v)=Au+Av=T(u)+T(v)

T(cu)=A(cu)=cAu=cT(u)

for all vectors u,v in Rn and all scalars c.

•  Since a matrix transformation satisfies the two defining properties, it is a linear transformation

1. We have T(0)=0+1=1. Since any linear transformation necessarily takes zero to zero by the above important note, we conclude that T is not linear (even though its graph is a line).