[8] ([:]) x(Q)-(C)-C-(C)--(-)- E Suppose T: R2 R2 is a transformation defined by T() =...

  

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[8] ([:]) x(Q)-(C)-C-(C)--(-)- E Suppose T: R2 → R2 is a transformation defined by T() = except that T (Examples: T = T T = T 0 (a) (2 points) Prove or give a counterexample: for every vector in R2 and scalar c, we have T(cv) = cT (v) (Hint: Separate in two cases, when is of the form and when it is not.) V2 (b) (2 points) Prove or give a counterexample: for every vectors and win R2, we have T(+w) T(v) +T(w). (c) (1 point) Is T a linear transformation? = [8] ([:]) x(Q)-(C)-C-(C)--(-)- E Suppose T: R2 → R2 is a transformation defined by T() = except that T (Examples: T = T T = T 0 (a) (2 points) Prove or give a counterexample: for every vector in R2 and scalar c, we have T(cv) = cT (v) (Hint: Separate in two cases, when is of the form and when it is not.) V2 (b) (2 points) Prove or give a counterexample: for every vectors and win R2, we have T(+w) T(v) +T(w). (c) (1 point) Is T a linear transformation? =

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