Solution Found!
In Exercises 29 and 30, V is a nonzero finite-dimensional
Chapter 4, Problem 29E(choose chapter or problem)
In Exercises 29 and 30, V is a nonzero finite-dimensional vector space, and the vectors listed belong to V. Mark each statement True or False. Justify each answer. (These questions are more difficult than those in Exercises 19 and 20.)a. If there exists a set that spans V , then dim .b. If there exists a linearly independent set in V , then dim .c. If dim V = p, then there exists a spanning set of p + 1 vectors in V .
Questions & Answers
QUESTION:
In Exercises 29 and 30, V is a nonzero finite-dimensional vector space, and the vectors listed belong to V. Mark each statement True or False. Justify each answer. (These questions are more difficult than those in Exercises 19 and 20.)a. If there exists a set that spans V , then dim .b. If there exists a linearly independent set in V , then dim .c. If dim V = p, then there exists a spanning set of p + 1 vectors in V .
ANSWER:Solution 29EStep 1 of 3Consider is a finite dimensional vector space.Let be non-zero.And consider the vectors listed belong to vector space (a)Consider the statement:If there exists elements set that spans then Objective is to identify whether the statement is true or false.According to spanning set theorem, to the set and produce a basis for vector space This basis will not have more than elements in it.So, we have the result Hence, the given statement is true.