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Determine if the statement is true or false, and justify your answer. If T(x) and T(x) are onto linear transformations from R to RM,

 

Determine if the statement is true or false, and justify your answer. If T(x) and T(x) are onto linear transformations from R to RM, then so is W(x) = T(x) + T(x). True, by the definition of linear transformation. True, by the definition of linear transformation and the definition of onto. False. Consider T(x) = T(x), where T is onto. False. Consider T(x) = -T(x), where T is one-to-one. False. Consider T(x) = -T(x), where T is onto.

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