# Previous answers holtlinalg1 31031 suppose that for

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T ( x ) = A A = 1 5 4 19 2 14 x T is one-to-one. T is onto. T is both one-to-one and onto. T is neither one-to-one nor onto. n = 3 > m = 2, 1 5 0 4 19 0 2 14 0 ~ 4 R 1 + R 2 R 2 R 1 + R 3 R 1 5 0 0 1 0 0 4 0 ~ 4 R 2 + R 3 R 1 5 0 0 1 0 0 0 0 2 3 3 T ( x ) = A x = 0
T ( x ) = A A = 1 2 4 3 7 5 2 4 3 x , 2 3 2 3
9. 3/3 points | Previous Answers HoltLinAlg1 3.1.031. Suppose that for the given A . Sketch a graph of the image under T of the unit square in the first quadrant of R 2 . T ( x ) = A x A = 1 7 9 1
Solution or Explanation
10. 3/3 points | Previous Answers HoltLinAlg1 3.1.034. Find an example that meets the given specifications. A linear transformation T : R 2 R 3 such that T ( x ) = 1 1 1 3 1 4 [0,1;0,3;0,4] x T = 0 1 1 3 4 . x
11. 3/3 points | Previous Answers HoltLinAlg1 3.1.037. Find an example that meets the given specifications. A linear transformation T : R 2 R 2 such that and T ( x ) = 1 -2 4 1 [1,-2;4,1] x Solution or Explanation T = 2 1 0 9 T = . 1 4 7 8 T ( x ) = x 1 2 4 1
12. 1/1 points | Previous Answers HoltLinAlg1 3.1.040. 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. Solution or Explanation = x 1 + x x 1 T . 13. 0/1 points | Previous Answers HoltLinAlg1 3.1.046. 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 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 x 1 x 2 x 1 T . T . T = x 1 + x x 1 2