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: 96/45
Step-by-step explanation: The answer is 96/12 because to divide fractions you reciprocate the second fraction and turn it into a multiplication problem.
8 times 12 = 96
9 times 5 = 45
96/45
Answer:
144.2 cm
Step-by-step explanation:
Length of the iron rod is 7.4cm
Radius is 3.1m
Therefore the surface area can be calculated as follows
= 2πrl
= 2×3.142×3.1×7.4
= 144.2 I'm
Hence the surface area is 144.2cm
Answer:
0.5, 80%
Step-by-step explanation:
Answer:
Step-by-step explanation:
h has to be 2 or more since there is at least 2 hours.
