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).
If you would like to know how many people attended the reunion last year, you can calculate this using the following steps:
125% of last year's attendance is 160 people
125% of x is 160
125% * x = 160
125/100 * x = 160 /*100/125
x = 160 * 100 / 125
x = 128 people (last year)
Result: 128 people attended the reunion last year.
9514 1404 393
Answer:
Step-by-step explanation:
To find miles per hour, divide miles by hours:
(15 mi)/(3 h) = 15/3 mi/h = 5 mi/h
__
To find distance, multiply speed by time.
(5 mi/h) × (10 h) = 50 mi
Answer:
B
Step-by-step explanation:
Communitive only works with multiplication and addition. It states that if you have something adding or subtracting something switched around, they are the same. B has that so the answer is B
Can I have Brainliest?
The correct answer should be steeper