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 tr(A)
is defined as the sum of all of its diagonal entries, i.e., tr(A) = X
n
i=1
aii. We
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
.
1