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>.
The correct answer is C.) (y|y > -4).
In order to find the range, we look for the possible numbers that y can be. In this case, you'll see the lowest the number goes is -4 and it continues up forever. Therefore, the answer is that y has to be greater than -4.
Answer:
0.375 litres
Step-by-step explanation:
Given that:
Total amount of lemonade held by pitcher = 3 litres
Number of people in which lemonade is to be given equally = 8
Amount of Lemonade received by each person will be:
Total amount of lemonade / number of persons
3 litres / 8
= 0.375 litres
Each person receives 0.375 litres of lemonade
Make the length x+4 and the width x and then make a formula x(x+4)=21
then u ll get x^2+4x-21=0 and then solve for x ..... the width is 3
Answer:
the slope is undefined
Step-by-step explanation:
slope = y2 - y1
___________
x2 - x1
slope = (-10-0) / {-4 - (-4 ) }
slope = -10 / (-4 + 4)
slope = -10 / 0
slope = undefined
note - Any number divided by zero is undefined
