1 2 3 4 5 6 7 Let o = be a permutation in S7. Find o³4. 3 7 6 2 4 1 5 In S7, are permutations a = (123) (246) (67) (135) and 3 = (5162) (123) (346) conjugate? Find the order of the element ((123) (45) , 3) in S5 × Z4.

Q: Find A-1 by forming [A|l] and then using row operations to obtain [I|B], where A 1 = [B]. Check that…

A:

Q: Let u = (2,6, 4) and 7 = (-1, -2, - 7). Compute the following: ū. v = vu - ||||²

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: et x, y E Z. We have (x+y)³ = (x+y)² (x+y) = (x² +2xy+y?)(x+y) = (x³+3x?y+3xy² + y³) = x³ + y3 od 3.

A:

Q: Let →u=⟨6,−4,−6⟩ and →v=⟨−5,−3,−6⟩. Compute the following:

A:

Q: Prove that: n² + 3n 1 →> 2n² + 1 2 You may use any results from lectures, but you must state them…

A: (.) Given,                We find the limit.

Q: Let ā= (2, 5, 7) and 6 = (1, 3, 4). (a - b) × (a + b) = X (3,16,33) X

A:

Q: Why does the fact that the orders of the elements of A4 are 1, 2, and3 imply that |Z(A4)| = 1?

A: Given: The orders of the elements of A4 are 1, 2, and 3.We need to signify the given fact to imply…

Q: (15) Let a, b = Z. Prove that if a is divisible by 4 and b is divisible by 4, then: (a) ab is…

A:

Q: Suppose the multiplication cx is defined to produce (cx1, 0) instead of (cx1, cx2 ). With the usual…

A: The multiplication cx where x∈ℝ2 is defined as cx=cx1, 0 because x=x1, x2 where x1 and x2 belong to…

Q: ) Express the pern 2546 1 product of the generators Wo=(12), `wa=(13), W1# (17) as a (125)(3 4 6 7)…

A: The generator of the permutation group S7 are given by: w2=1,2, w3=1,3, w4=1,4, w5=1,5, w6=1,6,…

Q: The permutations p= p and q in So have the two-line symbols 1 2 3 4 5 6 15 2 3 4 6 1 2 3 4 5 6 4 6 2…

A:

Q: If, (V₁ X V₂) · V3 = 6.5 then what is (V3 X V₁) - V₂? ○ (0,0,0) Cannot be found with the given…

A:

Q: If n = 12 m (me N), prove that "C₂ (2+√3)² "Co- - + "C4 (2+√√3)4 n "C6 (2+√3)6 ·+···=(-

A:

Q: Let B = -3 {CHEMED} 0 Find [x]s 3 3 and x = -8 23

A:

Q: 2. Let A = - (37 (c) BC (d) CA (e) AAT (0 n B = Evaluate the following products: (a) AB (b) A² C= 3…

A: We are given with the multiple number of subparts answer according to the guudeline

Q: 2. Find the LU factorizations of and 20 5 2 -6 3 -13 -3 4 9 16 17 2 4 -6 2 13 9 دن و ان 5 4

A:

Q: 1) Name the polynomial a) 3x? + 9x - 1 b) 2x* - 9x? - 1

A: a) 3x2+9x-1The above polynomial has a degree 2⇒It is quadratic polynomial

Q: 2. (a) Show that (z − 1)(26 + 25 + 24 + z³ + z²+z+1) = z7 - 1. (b) Show that if ¢ is a 7th root if…

A:

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.