What does it mean for a temperature to be below zero? Provide an example.
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Answer:
Step-by-step explanation:
REcall the following definition of induced operation.
Let * be a binary operation over a set S and H a subset of S. If for every a,b elements in H it happens that a*b is also in H, then the binary operation that is obtained by restricting * to H is called the induced operation.
So, according to this definition, we must show that given two matrices of the specific subset, the product is also in the subset.
For this problem, recall this property of the determinant. Given A,B matrices in Mn(R) then det(AB) = det(A)*det(B).
Case SL2(R):
Let A,B matrices in SL2(R). Then, det(A) and det(B) is different from zero. So
.
So AB is also in SL2(R).
Case GL2(R):
Let A,B matrices in GL2(R). Then, det(A)= det(B)=1 is different from zero. So
.
So AB is also in GL2(R).
With these, we have proved that the matrix multiplication over SL2(R) and GL2(R) is an induced operation from the matrix multiplication over M2(R).
In this case we have an ARM fixed for 6 years and adjust after the initial first 6 years every 2 years after. The basic idea behind a ARM is that the interest changes periodically, but since our ARM is fixed for 6 years, our going to calculate the monthly payment during the initial period using the formula: 
where
is the monthly payment
is the amount
is the interest rate in decimal form
is the number years
First we need to convert our interest rate of 4% to decimal form by dividing it by 100%:
We also know from our question that
and 
, so lets replace those values into our formula to find the monthly payment:
We can conclude that the monthly payment during the initial period is $1071.58<span />
where
First we need to convert our interest rate of 4% to decimal form by dividing it by 100%:
We also know from our question that
We can conclude that the monthly payment during the initial period is $1071.58<span />