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Let V and  W be vector spaces over the field F. Let  T and U be linear transformations from V into W. The function (T+ U)  defined by                          (T+U)(?) = T? + U?

Let V and  W be vector spaces over the field F. Let  T and U be linear transformations from V into W. The function (T+ U)  defined by                          (T+U)(?) = T? + U?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section: Chapter Questions
Problem 16RQ
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Let V and  W be vector spaces over the field F. Let  T and U be linear transformations from V into W. The function (T+ U)

 defined by
                         (T+U)(?) = T? + U?
 is a linear transformation from V into W. If c is any element of F, the function (cT) defind by
                             cT(?) = c(T?)

 is a linear transformation from V into W. The set of all linear transformationsfrom V into W, together with the addition and
 scalar multiplication defined above, is a vector space over the field F

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