Answer: .
Step-by-step explanation:
Step-by-step explanation:
=11/3×1/14
=3.67×0.07
=0.2568
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:
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Answer:
The inverse is 1/2x -3/2
Step-by-step explanation:
y =2x+3
Exchange x and y
x = 2y+3
Solve for y, subtracting 3 from each side
x-3 = 2y+3-3
x-3 =2y
Divide each side by 2
(x-3)/2 = 2y/2
1/2x - 3/2 =y
The inverse is 1/2x -3/2