Advance Math question and answers for July 01, 2023
- Q Let A be a square matrix defined by\( A =\begin{pmatrix}2&-3&1\\ 1&-2&1\\ 1&-3&2\end{pmatrix} \)(a) Find the characteristic polynomial of A.(b) Show that A is diagonalizable then diagonalize it.(c) Write $A^n$ \hspace{2mm}...
- Q The following are the Jordan Canonical Form of linear transformations. Find the characteristic polynomial, minimal polynomials, the algebraic multiplicity, geometric multiplicity and the index of each of the eigenvalues of L.B=\(...
- Q Let \( A\in M_n(\mathbb{R})\hspace{2mm} \) and\( \hspace{2mm} m_A(\lambda)\hspace{2mm} \) be its minimal polynomial. Let f be a polynomial satisfies\( \hspace{2mm}f(A) = 0. \hspace{2mm} \)Show that\( \hspace{2mm} f(\lambda) \hspace{2mm} \)is divisible...
- Q Find the characteristics and the minimal polynomial of the following matrices over \( \mathbb{R} \), then deduce the their corresponding Jordan Canonical Form J.B=\( \begin{pmatrix}2&-1&-1&2\\ 0&1&-1&2\\ 2&-5&-1&6\\ 1&-3&-2&6\end{pmatrix} \)
- Q How do you calculate the probability of compound events?
- Q Prove that in a finite cyclic group, each subgroup has size dividing the size of the group. Conversely, given a positive divisor of the size of the group, there is...
- Q What is the number of group homomorphisms from z12 to z13?
- Q Solve the differential equation with details explaination :x²y\" + 6xy' - 24y=x^9
- Q The number of involutions in G is |G|/4, and every right coset of a Sylow 2-subgroup S of G not contained in NG(S) contains exactly one involution.
- Q What x values is the function concave down if  f(x)=15x⅔+5x ?
- Q Find dy/dx and d2 y/dx2 . For which values of t is the curve concave upward?13. x = et , y = te-t
- Q A population of squirrels living in a forest with a carrying capacity of 2600.(assume logistics growth with constant k=0.9yr)(a)find a formula for the squirrels population p(t) assuming an initial population...
- Q y'=?2x+y+1general solution of differential equation
- Q The United States Postal Service (USPS) uses 11-digit serialnumbers on its money orders. The first ten digits identify thedocument, and the last digit is the check digit. The check digit...
- Q 1.Calculate the monthly payments on a home loan for $200, 000 at anAPR of 5.1% if the loan is for...a) 10 yearsb) 15 yearsc) 30 yearsThen recalculate the payments if...
- Q we are given n chips which may be working or defective. Aworking chip behaves as follows: if we connect it to another chip,the original chip will correctly output whether the...
- Q Prove that strongly connected" is an equivalence relation onthe vertex set of a directed graph
- Q (A) Using a straight edge, sketch the [1?23?] direction within acubic unit cell and label start and end points as well as x, y, andz axes. (B) Using a straight...
- Q Developing filters using convolution theorem and FourierTransform.You have been hired as an Engineering Mathematician at aconsulting firm located in Saint Louis. On your first job, you havebeen asked to mathematically...
- Q Solve the initial value problem11. xdx?y2dy=0, y(0)=112. dydx=yx, y(1)=?216. dydx=sinxy, y(0)=217. xy?=?1?y2, y(1)=023. Mr. Ratchett, an elderly American, was found murdered in histrain compartment on the Orient Express at 7...
- Q 3) consider computing e^x-1/xa) Explain when and why a loss of significance can happen.b) show how you can remedy the problem. Hint: use a Taylorseries.
- Q Let S be a subset of a vector space V . Show that span(S) =span(span(S)). Show that span(S) is the unique smallest linearsubspace of V containing S as a subset,...
- Q Find the steady-state current ip(t) in anLRC-series circuit when L = 1/2 h, R = 20 ?, C = 0.001 f,andE(t) = 100 sin(60t) + 300 cos(40t) V.
- Q Show that, for each of the following fields, it is impossible todefine an order relation ? that would make it an ordered field: (a)The set {0, 1} with addition and...
- Q Given a scalar fifield ?(x, y, z)=3x2-yz and a vectorfield F(x, y,z)=3xyz2+2xy3j-x2yzk.Find:(i)F.??.(ii)F×??.(iii)?(?.F).
- Q You are planning on flying out of an airport on a trip. Theairport parking garage charges $6 per day for the first four days,$4 per day for the next three...
- Q If V is a linear space and S is a proper subset of V, and wedefine a relation on V via v1 ~ v2 iff v1 - v2 are in...
- Q Analyzing Transactions Using the Financial Statement EffectsTemplate Following are selected transactions of Mogg Company.Record the effects of each using the financial statement effectstemplate. Shareholders contribute $10,000 cash to the business...
- Q Let Q(t)=x^2. Find a formula for the slope of the secant lineover the interval [9,t] and use it to estimate the slope of thetangent line at t=9t=9. Repeate for the...
- Q Solve the differential equation. x''(t)+2x'(t)+5x(t) = 2
- Q Prove the following test: Let {xn} be a sequence andlim |Xn| ^1/n = L1. If L< 1 then {xn} is convergent to zero2. If L> 1 then {xn} is divergent
- Q show that for any n the matrix ring M_n(F) is simpleover a field F.show your work. Do not use quotient rings!
- Q what category of analytics does management science mainly focus andwhat does it involve doing?
- Q Construct a derivation (for the following argument) fromthe premise to the conclusion, only using these :(&I, &E,?I, ?E, ? I, ? E ,? I, ? E,? I, ? E)(a) Premise...
- Q View S3 as a subset of S5 in the obviousway. For ?, ? ? S5, define ? ? ? if ?? -1 ?S3.(a) Prove that ? is an equivalence relation...
- Q Consider the integers from 1 to 10. Give the set of pairs (a, b)that corresponds to relation a ? b mod 1.
- Q Solve equations1.) y'-y=t/y2.) y'-(1/t)y=y2sin(t)3.) y'+y=y2cos(t)4.) y'-2y=cos(t)/(y1/2)
- Q . Solve the Initial value problem by using Laplace transforms: ??? + 3? ? + 2? = 6? ?? , ?(0) = 2 ? ? (0) = 8
- Q 1.Determine whether S spans V . Justify your answers.V = C ^0 [?1, 1] (the vector space of continuous functions on[?1, 1]) and S = {1, t, t2 , t3...
- Q Find the dimensions of the following linear spaces.(a) The space of all 3×4 matrices(b) The space of all upper triangular 5×5 matrices(c) The space of all diagonal 6×6 matrices
- Q The n- dimensional space is colored with n colors such thatevery point in the space is assigned a color. Show that there existtwo points of the same color exactly a...
- Q Give a direct proof for the 2nd Isormorphism Theorem ofbi-modules over rings.
- Q Solve d) and e). I have provided answer for c)too required in e)Winkler Furniture manufactures two different types of chinacabinets: a French provincial model and a Danish Modern model. Eachcabinet...
- Q Use method of Frobenius to find one solution of Bessel'sequation of order p: x^2y^''+xy^'+(x^2-p^2)y=0
- Q Question 12.20 – Use these data - incidents of reports ofunderage drinking – to perform the following: “Dry” campus, stateschool: 47, 52, 27, 50 “Dry” campus, private school: 25, 33,...
- Q Question 2: Preparation and Presentation of the Income StatementFlexible and Confused Limited has just employed you as the newfinance director. The first task you have been assigned to completeis to...
- Q 3,1. Suppose that the price of an asset at close of tradingyesterday was $350 and its volatility was estimated as 1.4Voperday. The price at the close of trading today is...
- Q give one of the major application of graph theory in real life
- Q Suppose your instructor asked you to look at the influence ofage (X) on automobile insurance premium rates (Y). List threevariables you might control for in your regression analysis and whyyou...
- Q Are {4cos^2(x),cos(2x),5} linearly independent? prove withoutwronskian
- Q Find the special fundamental matrix for the following systemsuch that ?(0) = I.x' = row 1 ( 4 3 )row 2 ( 3 -4 ) * x
- Q Explain using complete sentences the advantages of providing anEXACT solution to a quadratic equation rather than a decimalapproximation.
- Q Solve the differential equation by Laplace transformy^(,,) (t)-2y^' (t)-3y(t)=sint where y^' (0)=0,y=(0)=0
- Q Let A be a collection of sets,then We defined A’ = Union of all elements of A.Definition: If A = NOT the unionof C and D , where C and...
- Q x^2=ln(cy^2) Find the perpendicular orbits of the family ofcurves
- Q 4.(12 pts) A 20,000 liter tank is initially half full with10,000 liters of 2% nitric acid. A solution of 5% nitric acid ispumped in at a rate of 30 liters...
- Q Show that if a, b are positive integers and d = hcf(a, b), thenthere are positive integers s, t such that d = sa ? tb.
- Q 2. (16 pts) Use binary modular exponentiation to find 45 mod 84.(Use either table approach taught in slides or the pseudocodealgorithm.)3. (20 pts) Use the Euclidean Algorithm to find the...
- Q A leading UK Chocolate Brand has seen a downturn in sales due tonew competition in themarket. Analysis work has shown the need for a customer loyaltyprogramme. You have beentasked with...
- Q The number of words defined on pages randomly selected from adictionary are given below. Find the range and standard deviationfor the set of numbers.77 62 43 79 41 68 69...
- Q Consider the optimization problem of the objective function f(x,y) = 3x 2 ? 4y 2 + xy ? 5 subject to x ? 2y + 7 = 0. 1. Write...
- Q Given a complicated lim x ? af (x), how do you quickly determinewhich items aresignificant and which items are negligible —¿ quick guess in 5seconds? Degree (or order) of largeness....
- Q Assume the carrying capacity of the earth is15billion. Use the 1960s peak annual growth rate of2.1?%and population of3billion to predict the base growth rate and current growth ratewith a logistic...
- Q Which of the following statements are true and which arefalse?(a) Assume that we are implementing AES or a similar system onan RFID tag. When calculating the ASIC cost, one of...
- Q Constant Yield Harvesting. In this problem, we assume that fishare caught at a constant rate h independent of the size of the fishpopulation, that is, the harvesting rate H(y, t)...
- Q Assume we are flipping 1000 fair coins. What can you say aboutthe probability that you will get at least 3/5 of them to be heads?Compare the 3 bounds (Markov, Chebyshev,...
- Q What do you know about how math and historical developments are related? Share any information you already have about the topic.Are there any questions you still have?Do you believe that...
- Q Allow the main process to generate a text file containing thetext of this assignment.The main process will then create two other processes and passto them the name of the file...
- Q Write theclass MultiDimListaccording to thefollowing requirements:1.Each node contains3 fields of data (Name, ID, Mark out of 100).2.Each node will havetwo pointer: nextMark, nextName3.The nodescan besortedin an ascendingway based onthe Mark...
- Q 5. (a) Let f : R {?1} ? R, f(x) = x+1. Show that f isinjective, but not surjective.(b) Suppose g : R{?1} ? R{a} is a function such that...
- Q The neighborhood of a vertex in a graph consists of the vertexitself, together with all vertices that are connected to it by anedge. Each graph has a variable xi associated...
- Q What does it mean for a relation is a partial orderrelation?
- Q Combined, there are 207 ?Asians, Africans,? Europeans, andAmericans in a village. The number of Asians exceeds the number ofAfricans and Europeans by 65. The difference between the number ofEuropeans and...
- Q Represent with the language of First Order Predicate Logic thefollowing proposition:"If S is an arbitrary set of objects for which there is anassociative binary operation * (function) with the following...
- Q For each of the following differential equations, find theparticular solution that satisfies the additional given property(called an initial condition).y'y = x + 1
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