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:
(6,9)
Step-by-step explanation:
the x place is counting by 2 and the y place is going up by 3
12 beacuse he has enough to to it to ur soo good for the game to play it and ur soo fun
If he eats 6 loaves in 8 days, that means he ate 0.75 of a loaf each day. (6 divided by 8 = 0.75)
In a 12 day trip,
# divided by 12 = 0.75;
so to undo division, you multiply.
12 x 0.75 = #
# = 9. So 9 loaves for 12 days.
Answer:
The volume of a triangular pyramid is 24 cubic inches. The base is a right triangle with a length
of 4 inches and height of 3 inches. What is the height of the pyramid, in inches?
Step-by-step explanation:
The volume of a triangular pyramid is 24 cubic inches. The base is a right triangle with a length
of 4 inches and height of 3 inches. What is the height of the pyramid, in inches?
The volume of a triangular pyramid is 24 cubic inches. The base is a right triangle with a length
of 4 inches and height of 3 inches. What is the height of the pyramid, in inches?
