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…

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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: snip

A: In a matrix the horizontal arrangements of elements is called rows…

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.

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

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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

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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: 7. 2) Write the difference equation for the systems shown below. ii) Find yon) / xen). yon) x(n) 3…

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Q: Q. (a) Find an equation of the tangent plane to each surface at the given point. (b) Find symmetric…

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

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Q: The number of the element(s) of order 2 in Z3 O Z6 O 2 3

A: Given  ℤ3⊕ℤ6

Q: Let a E R which expressions are correct? and give the justification why they are part of the Borel o…

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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: Find all (p, q, r) such that ((p + -4) evaluates to 1.

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Q: Let C= (replace the third column with the second column C2 C.). Show that |Cl=-IAl (Home work) lumn…

A: As two questions are given , I will do only the first one : C=13211-1243…

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: Let = [1, -1, 1], [-2, -1, 3] and = [-1, 2, 2]. Find (u ×7)•w: O-14 07 O 10 Does not exist

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Q: Show that r3 + 3x² – 8 is irreducible over Q.

A: Here Q is a field and f(x)= x³+3x²-8 is of degree 3. Then by ROOT TEST we can say that f is…

Q: [-1 2 Q5/ Let A = |-2 5 -3] 3 4 ,then the C33 is 0 1 -1 -10 -2

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Q: Find the generalized union and intersection: 3) A = {1,2,3,...} A₂ = {x|x = 22m where m eset of…

A: Given that, Λ={1,2,3,…} Λλ=x|x=2λm where m∈set of integers from -λ to +λ The objective is to find…

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…

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

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Q: (7) For any nonzero a, b € Z, the gcd(a, b) divides the lem(a, b). (8) If r, y € Z and 3 divides ry,…

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Q: ne order of the element 16+ in Z24/ is None of the choices 8.

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Q: The population of a community is known to increase at a rate proportional to the number of people…

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Q: 23) Expand: 2r(x² +1)-(x² + 5x - x - A) x² - x² - 3x - 7 B) x* + 2x² - 3x -7 C) x² +x² - 3x +7 D) x*…

A: The given expression is2xx2+1-x3+5x-x4-7 expand the given expression and then simplify to obtain the…

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

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Q: Q2/ prove [A] [A] = [I] if [2 4 -5 [A]= 2 7 1 3 4

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

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Q: Find all the conjugacy classes of D4.

A: We have to find conjugacy Classes of the Dihedral Group, D4

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. Show that if 8=(AB)- then - > N - - (AB)² + (aß)² – (αB)² – (AB)² = [(A) − (α)] [(B) − (ß)] +…

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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

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Q: - ₂ F₁ (-m. a + m;c; x) = +++(c + m) -r (c) dm [x²+m-¹ (1-x)²-c+m] m

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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…

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Q: -1 -1 01 3 31 [4 The (1,2) – entry of, 0 is 12 1 2 (A -1 B) 4 c) 1 D) 14

A: We want to find (1, 2) entry

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.