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).
y - 1 = ⁵/₆(x - 4)
y - 1 = ⁵/₆(x) - ⁵/₆(4)
y - 1 = ⁵/₆x - 3¹/₃
+ 1 + 1
y = ⁵/₆x - 2¹/₃
⁻⁵/₆x + y = ⁵/₆x - ⁵/₆x - 2¹/₃
-6(⁻⁵/₆x + y) = -6(-2¹/₃)
-6(⁻⁵/₆x) - 6(y) = 14
5x - 6y = 14
Answer:
3 trips
Step-by-step explanation:
We would divide the amount of riders the roller coaster could take in a single trip by the total number of riders to determine how many trips it can make.
max amount of riders/total riders
72/24 = 3
Hence, the rollercoaster made 3 trips.
Answer:
equation of the line is y=x+1
Step-by-step explanation:
the equation of a line has the form y = mx + b
while m is for the slope and b is for the y-intercept.
you can see from the graph that the line intercepts the y-axis at y=1 this is the b.
you can get the slope of the graph by taking two points from the graph lets say (1, 2) and (3, 4) then using this formula:
<h2>
</h2>
in our case it will be:
then just substitute the values for m and b.
Given inequality
=> −2(x+1)≥3x+8
=>
now multiply with - on both sides.
As we know now sign will change
=> 5x >_ -10
Now divide by 5 on both sides
=> x >_ -2
HOPE IT HELPED YOU.
