Give an example of a matrix with real-valued entries, whose eigenvalues are complex numbers.

Q: t A and B be arbitary n x n matrices. If B is invertible, prove that AB- = B-'A if and only if AB =…

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Q: Use Laplace transform to solve the given IVP. = cos 3t, x(0) = 2, ¿(0) = 5 6. * + 9x

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Q: Structural Engineers in an iron manufacturing company describe the results of deformation on the…

A: Given The data is as follows: 230.66, 233.05, 232.58, 229.48, 232.58

Q: The following are the number of cars sold per day at ABC Motor corporation during the past 500…

A: Using formula for probability is :- probability, P(X)= frequency total frequency And ,     Mean =…

Q: Draw a direction field for the differential equation y' = -y(2-y). Based on the direction field,…

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Q: You work in facilities at a small college and need to build a fence around an athletic field (see…

A: Form the equation and then use first derivative to maximize.

Q: (1–3cot.x)² dx cscx

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Q: 1. Without directly using the calculator, compute the first through fourth-order approximation of…

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Q: Write the equation in general form of the circle with center (-4,3) and radius V13.

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Q: Question 3 Suppose that Z₁, Z2,..., Zn are statistically independent. random variables. Define Y as…

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Q: dx ex -1

A: Let ex=t ⇒exdx=dt    dx=dtex          =dtt

Q: he random variable x has the following probability distribution: f(x) 25 1 20 .15 .30 4. .10 3.

A: Given data,

Q: ? dx = In|x| – e* + C ? S 2²+3xdx = 4 In 8 + C

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Q: 3. For an arbitary 2-by-2 system of equations ax + by =r cx + dy = s (a) Determine the LU…

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Q: Activity 3: Find Me! To further strengthen the foundations in solving permutations, you may search…

A: 1) the covered walk of a school is to be lined with flags. how many different arrangements are there…

Q: Find a function h and a real number s such that + S h(t)dt =x tan'x 4 S

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Q: 3. Using the subplot command, plot y=arc tan(x) at the top and y-arc cot(x) at the bottom for values…

A: A computer algebra system(CAS) can be used to plot a set of curves on the same window. The CAS can…

Q: eliminate arbitrary constants. Show complete solution. y= Ax + Bx²

A: The given solution of the differential equation is   Where A and B are arbitrary constant.

Q: II. Use Gaussian elimination in matrix form to solve the system. ( z+ 2y – 4z = 5 2x + y – 6z = 8 4x…

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Q: Show that the following functions satisfy Laplace's equation 0. dy? %3D (a) f(r, y) = r*y – xy³

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Q: in rectangu -6

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Q: Problem 5: The components of a vertical force P are Q = 200 N and S as shown in Figure 1.7 - 5. 1.…

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Q: a. What is the distribution of U = Y?? Explain using the concepts discussed in class. b. What is the…

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Q: The graphs of f and g are given. ,State the values of f(-4)and g(3). 1. For what values of x is f(x)…

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Q: Question 3. Show your working in each case: (a) Find all the cluster points of the set M = {÷ +: m,n…

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Q: x2 • X is a Rayleigh random variable such that f x(x) = transformation is made such that Y = X². xe…

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Q: Find the determinant using Gaussian Elimination Methoc 5w + 6x - 5y + 11z = 7 10w + 36x + 10y – 17z…

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Q: Let R* denotes the set of positive real numbers and let f: R+ R+ be the bijection defined by ƒ (x) =…

A: In this solution, we will examine the properties of the binary operation ⊗ on the set of positive…

Q: 2. How many unique 3 digit codes can be created from the 5 digits {1, 2, 3, 4, 5} if repetitions are…

A: A permutation of a set is defined as an arrangement of its members into a sequence or if the set is…

Q: 3 dx (x2–1)2

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Q: In order, arrange the steps of the solution of the V3 +6x2 + 9xdx from the start until reaching the…

A: We have given an indefinite integral. In indefinite integral, we add the constant term, C (known as…

Q: Determine the minimum sample size if the Margin of error is 0.045, with confidence level 95%, and p…

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Q: Consider the vector field Ĥ(x, y, z) = (y², x, z²). Let S3 be the portion of the paraboloid 2 = x² +…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.