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).
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Answer:
b
Step-by-step explanation:
i aint never seen two pretty best friends its always one of em gotta be ugly
Answer:
10 kph
Step-by-step explanation:
Find the speed of the current of the river.
20/(20 - c) + 180/(20 + c) = 8
20(20 + c) + 180(20 - c) = 8(400 - c^2)
8c^2 - 160c + 800 = 0
8(c^2 - 20c + 100) = 0
8(c - 10)^2 = 0
c = 10
The speed of the current of the river is 10 km/hour.
Answer:
Step-by-step explanation:
heyq
The correct answer is:
7/10
Explanation:
Finding the totals of each column and row, we find:
There are 3+2+1 = 6 children in the baseball league.
There are 7+2+1 = 10 children in the softball league.
There are 3+7 = 10 children in the 7-9 division.
There are 2+2 = 4 children in the 10-12 division.
There are 1+1 = 2 children in the 13-15 division.
There are a total of 10+6 = 16 children.
We start with the information that the team is a member of the softball league. There are 10 children in this league; this is the denominator of the probability.
There are 7 children in the 7-9 division that are in the softball league. This gives us the probability 7/10.
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