No. Consider defined as .

Yes, that is the definition of linearity.b.) If T maps Rn into Rm, and if T(c1u +c2v) =c1T(u) + c2T(v) for all scalers c1 and c2 and for all vectors u and v, then T is linear. True as this represents the addivtivity and is alinear transformation by definition. Am I right?

c. ) There is only one linear transformtion T : Rn ->Rn such that T(-v) = -T(v) in Rn. Not sure if this is true or false.Anylinear transformation has this property.

Yes. If it means thus thus thus is the zero transformation.d.) there is only one linear transformation T: Rn -> Rn for which T (u + v) = T (u-v) for all vectors u and V in Rn. ???

Is it true that ?e.) if vo is a nonzero vector in Rn, then the formula T(v) = v0 +v defines a linear operator in V. Still nto understanding the meaning of linear operator. Help!