Write "T" or "F" to indicate which of the properties are True or False. When the property is false, provide a counterexample in the space provided (if the answer is true, then place 0 in all boxes for the counterexample). Note that all transformations only use real values. 1) Let 7 [a b] = T a) b) and U = C) and k = d) -la + (-1) b + 3c + (-1) d la + 3b + 1c + 2d 2a + 2b +3c+(-1)d 2a + (-1) b+ (-1) c+(-1)d] : This transformation maps the zero vector to a zero vector. : This transformation is closed under addition. If this is false, a counterexample is given by: u = : This transformation is closed under scalar multiplication. If this is false, a counterexample is given by: u = : This transformation is a linear transformation.

Write "T" or "F" to indicate which of the properties are True or False. When the property is false, provide a counterexample in the space provided (if the answer is true, then place 0 in all boxes for the counterexample). Note that all transformations only use real values. 1) Let 7 [a b] = T a) b) and U = C) and k = d) -la + (-1) b + 3c + (-1) d la + 3b + 1c + 2d 2a + 2b +3c+(-1)d 2a + (-1) b+ (-1) c+(-1)d] : This transformation maps the zero vector to a zero vector. : This transformation is closed under addition. If this is false, a counterexample is given by: u = : This transformation is closed under scalar multiplication. If this is false, a counterexample is given by: u = : This transformation is a linear transformation.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.2: The Kernewl And Range Of A Linear Transformation

Problem 61E

See similar textbooks