I need help very fast please!
2 answers:
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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:
85.9 (to the nearest hundredth)
Step-by-step explanation:
1 radian = 180°/
Therefore, 1.5 radians = 1.5 x (180°/) = 270/
= 85.9 (to the nearest hundredth)
ANSWER
C. 58°
EXPLANATION
The sum of the interior angles of a triangle is 180°.
We sum all the three angles to obtain,
.
We group like terms to get,
.
Simplify,
.
Combine like terms to get,
.
Simplify,
.
Divide both sides by 32 to get,
.
We substitute the value of x into the expression for
.
This implies that,
.
.
.
The correct answer is C