Please help me with this question

Consider the following sets of matrices: M2(R) is the set of all 2 x 2 real matrices; GL2(R) is the subset of M2(R) with non-zer

defon

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

$\text{det(AB)} = \text{det}(A)\text{det}(B)\neq 0$ .

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

$\text{det(AB)} = \text{det}(A)\text{det}(B)=1\cdot 1 = 1$ .

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).

7 0

3 years ago

Employment data at a large company reveal that 74% of the workers are married, 42% are college graduates, and that 56% are marri

ValentinkaMS [17]

Answer:

(E) None of these above are true.

Step-by-step explanation:

Married = 74% or 0.74

College graduates = 42% or 0.42

pr(married | college graduates) = 0.56

(A) These events are pairwise disjoint. This is false. Pairwise disjoint are also known as mutually exclusive events. Here we can see that both events are occurring at same time.

(B) These events are independent events. This is also false.

(C) These events are both independent and pairwise disjoint. False

(D) A worker is either married or a college graduate always. False

Here Probability(A or B) shall be 1

= Pr(A) + Pr(B) - Pr( A and B) = 0.74 + 0.42 - 0.56 * 0.42 = 0.9248

This is not equal to 1.

(E) None of these above are true. This is true.

8 0

4 years ago

>

kondor19780726 [428]

Answer:

23 degrees

Step-by-step explanation:

Find the diagram attached

The sum of angle on the straight line is 180°

103+3x+15+x+10 = 180

128+4x =180

4x = 180-128

4x = 52

x = 52/4

x = 13

The measure of the angle of the intersection between Derby Drive and Rosemont is x+10

= 13+10

= 23 degrees

Hence the measure of the angle is 23 degrees

5 0

3 years ago

ASAP<br> -WILL MARK BRIANIST

Thepotemich [5.8K]

Answer:

C and D

Step-by-step explanation:

C and D are the answers because when you simplify D which is 95/100 × 6 you get 0.95×6 which is the same thing as c

8 0

3 years ago

1. William earns $134,644.80 per year, and has his federal taxes withheld from each weekly check. In addition, a total of $53.60

SashulF [63]

I only have the answer for 3 and i believe it is 20,090

3 0

3 years ago