Answer:
Recall that a relation is an <em>equivalence relation</em> if and only if is symmetric, reflexive and transitive. In order to simplify the notation we will use A↔B when A is in relation with B.
<em>Reflexive: </em>We need to prove that A↔A. Let us write J for the identity matrix and recall that J is invertible. Notice that 
. Thus, A↔A.
<em>Symmetric</em>: We need to prove that A↔B implies B↔A. As A↔B there exists an invertible matrix P such that 
. In this equality we can perform a right multiplication by 
and obtain 
. Then, in the obtained equality we perform a left multiplication by P and get 
. If we write 
and 
we have 
. Thus, B↔A.
<em>Transitive</em>: We need to prove that A↔B and B↔C implies A↔C. From the fact A↔B we have and from B↔C we have 
. Now, if we substitute the last equality into the first one we get
.
Recall that if P and Q are invertible, then QP is invertible and 
. So, if we denote R=QP we obtained that
. Hence, A↔C.
Therefore, the relation is an <em>equivalence relation</em>.
Answer:
9 weeks
Step-by-step explanation:
Answer:
1139.2 hours
Step-by-step explanation:
6.40 x 178 = 1139.2
A) about 45
If we sold around 90, it would NOT be shown in the graph. And starting on June 15, we sold (per say 50). On June 19 we end with approximately 100. So 45 would be the most probable answer.
Hope this helps!
Answer:
- (2^9)
Step-by-step explanation:
-(2^6)(2^3)
We know a^b * a^c = a^( b+c)
- ( 2 ^ (6+3))
- (2^9)
