TBA 8PLEASE ONLY ANSWER 8 THANK YOUALSO MAKE SURE YOUR ANSW

TBA 8+++++++++++++PLEASE ONLY ANSWER # 8. THANK YOU!!!!!!!!!!!!!!!!!!!!!!!!!ALSO, MAKE SURE YOUR ANSWER IS LEGIBLE AND YOU WILL GET A THUMBS UP!!!!!!!!!!!!!!

Mark each statement true or false and justify your answer. No justification, no credit. For questions that are not true/false, provide clear and complete solutions. Every linear transformation from R\" to R matrix transformation. 6. is a A mapping T : Rn Rm is one-to-one if each vector in R\" maps onto a unique vector in R\" 7. 8. Why is the question \"Is the linear transformation T onto?\" an existence question? Explain clearly and completely.

Solution

Let T: V->W be a linear transformation.

By defintion, T is onto if given any w in W there exists a v in V such that Tv=w.

Hence \"T is onto\" is equivalent to the existence of a preimage of (every vector) w in W.

(Note: There is nothing special about T being a linear transfromation). The question and the answer make sense for any function f:X->Y , where X and Y are given sets. Linearity of T is irrelevant)