[SOLVED] MATH307-Individual Homework 4

Description

1. Textbook page 40, problem 1.
2. Textbook page 40, problem 5.
3. Let F be a field such as R or C and F^n×n be the set of all n × n matrices with entries chosen from F. Let A ∈ F, the trace of A, denoted by is defined as the sum of all of its diagonal entries, i.e., tr(A) = ^Xa_ii. We

i=1

know that F^n×n is a vector space over F. Prove that {A ∈ F^n×n|tr(A) = 0} is a subspace of F^n×n.