Question

If ? and ? are in ? and ??=??, we say that ? and ? commute....

If ? and ? are in ? and ??=??, we say that ? and ? commute. Assuming that ? and ? commute, prove the following: (2)

1. ?−1 and ?−1 commute.

2. ? and ?−1 commute. (HINT: First show that ?=?−1??.)

3. ???−1 commutes with ???−1, for any ?∈?.

4. ??=?? iff ???−1?−1=?.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
1. Suppose we have the following relation defined on Z. We say that a ∼ b...
1. Suppose we have the following relation defined on Z. We say that a ∼ b iff 2 divides a + b. (a) Prove that the relation ∼ defines an equivalence relation on Z. (b) Describe the equivalence classes under ∼ . 2. Suppose we have the following relation defined on Z. We say that a ' b iff 3 divides a + b. It is simple to show that that the relation ' is symmetric, so we will leave...
) In the following problems, let ? be a cycle of length ?, say ? =...
) In the following problems, let ? be a cycle of length ?, say ? = (?1?2 … ??). (a) Find the inverse of ?, and show that ? −1 = ? ? (b) Prove that ? 2 is a cycle iff ? is odd.
Let a, b, c be natural numbers. We say that (a, b, c) is a Pythagorean...
Let a, b, c be natural numbers. We say that (a, b, c) is a Pythagorean triple, if a2 + b2 = c2 . For example, (3, 4, 5) is a Pythagorean triple. For the next exercises, assume that (a, b, c) is a Pythagorean triple. (c) Prove that 4|ab Hint: use the previous result, and a proof by con- tradiction. (d) Prove that 3|ab. Hint: use a proof by contradiction. (e) Prove that 12 |ab. Hint : Use the...
We say that a point C (anywhere) on an axis that contains a vector AB ≠...
We say that a point C (anywhere) on an axis that contains a vector AB ≠ 0 ( and so A ≠ B), divides the vector AB ≠ 0 in ratio λ, if (AC/CB) = λ . This ratio is also called the simple ratio of the points A, B, C in the order denoted by {A, B; C}. So, when A ≠ B prove: (a) C is between A and B iff λ > 0. (b) C is outside...
Let V and W be vector spaces and let T:V→W be a linear transformation. We say...
Let V and W be vector spaces and let T:V→W be a linear transformation. We say a linear transformation S:W→V is a left inverse of T if ST=Iv, where ?v denotes the identity transformation on V. We say a linear transformation S:W→V is a right inverse of ? if ??=?w, where ?w denotes the identity transformation on W. Finally, we say a linear transformation S:W→V is an inverse of ? if it is both a left and right inverse of...
Question 1 a) To show that 3-CNF is NP-complete, we take some NP-complete problem, say SAT,...
Question 1 a) To show that 3-CNF is NP-complete, we take some NP-complete problem, say SAT, and find a polynomial-time reduction from SAT to 3-CNF. Illustrate a polynomial-time reduction that takes as input an input F of SAT F = (¬x1 ∨ x2 ∨ x3) ∧ (x4 ⇔ ¬x5) and outputs an input f(F) of 3-CNF so that f(F) is a “yes” instance of 3-CNF iff F is a “yes” instance of SAT. b) Let F be an input to...
If we are to have a square matrix (say B), and B = QR, where QR...
If we are to have a square matrix (say B), and B = QR, where QR is the QR factorization of B, Define C = RQ. We need to prove that B and C are similar, and how do we prove C is similar to B assuming that B is symmetric?
3. Use R Studio: Include R Code A commuter records 20 commute times to gage her...
3. Use R Studio: Include R Code A commuter records 20 commute times to gage her median commute time. The data has a sample median of 24 and is summarized in this stem-and-leaf diagram: stem(commutes) 2 | 111233444444 2 | 55569 3 | 113 If the data is appropriate for t.test, use that to compute a 90% confidence interval for the median. Otherwise use wilcox.test (perhaps after a transform) to compute a confidence interval for the median.
We say that x is the inverse of a, modulo n, if ax is congruent to...
We say that x is the inverse of a, modulo n, if ax is congruent to 1 (mod n). Use this definition to find the inverse, modulo 13, of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12. Show by example that when the modulus is composite, that not every number has an inverse.
Suppose that X1, X2, X3, X4 are iid N(θ,4). We wish to test H0: θ =...
Suppose that X1, X2, X3, X4 are iid N(θ,4). We wish to test H0: θ = 2 vs H1: θ = 5. Consider the following tests: Test 1: Reject H0 iff X1 > 4.7 Test 1: Reject H0 iff 1/3(X1 + 2X2) > 4.5 Test 3: Reject H0 iff 1/2(X1 + X3) > 4.2 Test 4: Reject H0 iff x̄>4.1 (xbar > 4.1) Find Type 1 and Type 2 error probabilities for each test and compare the tests.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT