10 33 points previous answers holtlinalg2 31034 find

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10. 3/3 points | Previous Answers HoltLinAlg2 3.1.034. Find an example that meets the given specifications. A linear transformation T : R 2 R 3 such that T ( x ) = x 11. 3/3 points | Previous Answers HoltLinAlg2 3.1.037. Find an example that meets the given specifications. A linear transformation T : R 2 R 2 such that and T ( x ) = x 12. 1/1 points | Previous Answers HoltLinAlg2 3.1.040a. Determine if the statement is true or false, and justify your answer. The range of a linear transformation must be a subset of the domain. T = . 0 1 1 3 4 T = 2 1 0 11 T = . 1 5 −9 10 True, by definition of the domain. True, by definition of the range. False. For instance T : R 2 R 2 defined by T = x 1 + x 2 has range( T ) = R , which is not a subset of R 2 , the domain of T . x 1 x 2 False. For instance T : R 2 R defined by T = x 1 + x 2 has range( T ) = R , which is not a subset of R 2 , the domain of T . x 1 x 2 x 1
13. 1/1 points | Previous Answers HoltLinAlg2 3.1.046a. Determine if the statement is true or false, and justify your answer. If are onto linear transformations from R n to R m , then so is T 1 ( x ) and T 2 ( x ) W ( x ) = T 1 ( x ) + T 2 ( x ). True, by the definition of linear transformation. True, by the definition of linear transformation and the definition of onto. False. Consider T 2 ( x ) = T 1 ( x ), where T 1 is onto. False. Consider T 2 ( x ) = − T 1 ( x ), where T 1 is one­to­one. False. Consider T 2 ( x ) = − T 1 ( x ), where T 1 is onto.
2/7/2018 UW Common Math 308 Section 3.1

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