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).
Answer:
The company's profit in 2007 was 11.088 millions
Step-by-step explanation:
This is a compound interest problem where the initial amount is 8.8 million, the interest rate is 6% and the time period is 4 years and it gets compounded yearly. So we can use the compound interest formula, that is given by:
A = P*(1 + r/n)^(n*t)
Where A is the final amount, P is the initial amount, r is the rate, t is the total amount of time and n is the number of times it gets compounded in one year. We can now use all the values that were given to us to find out the profit of the company.
A = 8.8*(1 + (0.06))^(4) = 8.8*(1.06)^16
A = 8.8*1.26 = 11.088 millions
So the company's profit in 2007 was 11.088 millions
Answer:
The figure above shows the graph of a function f with domain 0 ≤ x ≤ 4. Which of the following statements are true? Show Video ... If there is no c, where -2 < c < 2, for which f'(c) = 0, which of the following statements must be true? Show Video ...
Step-by-step explanation:
The best and most correct answer among the choices provided by the question is B.) 23,000
Hope this helps :)
