Is 70% of 80 the same as 80% of 70
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: 374416
Step-by-step explanation:
Given : A test requires that you answer first Part A and then either Part B or Part C.
Part A consists of 4 true false questions, Part B consists of 6 multiple-choice questions with one correct answer out of five, and Part C consists of 5 multiple-choice questions with one correct answer out of six.
i.e. 2 ways to answer each question in Part A.
For 4 questions, Number of ways to answer Part A =
5 ways to answer each question in Part B.
For 6 questions, Number of ways to answer Part B =
6 ways to answer each question in Part C.
For 5 questions, Number of ways to answer Part C =
Now, the number of ways to completed answer sheets are possible :_
Hence, the number of ways to completed answer sheets are possible = 374416