# Solution or explanation false w will be linear but

• Homework Help
• 8
• 98% (115) 113 out of 115 people found this document helpful

This preview shows page 7 - 8 out of 8 pages.

Solution or Explanation False. W will be linear, but not necessarily onto. Consider T 2 ( x ) = T 1 ( x ), where T 1 is onto. True, by definition of the domain. True, by definition of the range. x 1 T . False. For instance T : R 2 R defined by T = x 1 + x 2 has range( T ) = R 2 , which is not a subset of R , the domain of x 2 T . x 1 2 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 one-to-one.
14. 4/4 points | Previous Answers HoltLinAlg1 3.1.049. A linear transformation T : R 2 R 2 is called a dilation if for r > 1. (It is called a contraction (a) Find the matrix A such that r 0 0 r [r, 0; 0, r] (b) Let r = 2 , and then sketch the graphs of T ( x ) = r x 0 < r < 1.) T ( x ) = A x A = x = 3 if and Solution or Explanation (a) (b) . 1 T ( x ). A = r 0 0 r