Let A and P be a nxn matrices and P is invertible. Show that A and PA have the same rank

Q: 2. Solve the initial value problem 7¹ = [73] + [3] - X with X (0) = [1¹]

A: Initial value problem x'=-7-1045x+-43 with x0=-11 which is of the form x'=Ax+b

Q: ■ Prove that the function x) = { win = ²+ = = 0 x X 0, x f(x) satisfies the intermediate value…

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Q: Let the surface S be part of the cone z2 = x2 + y2 which is inside the cylinder x2 + y2 = 2y,…

A: Let the surface S be part of the cone z2 = x2 + y2  and inside the cylinder x2 + y2 = 2y, outside…

Q: Which of the following is a correct form of a particular solution of y" + 3y - 4y = 3 cos(2t)et +…

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Q: 2. Determine the Fourier series expansion of the periodic function f(x) f(x+2) = f(x), x E R. Use…

A: The given problem is to determine the Fourier series expansion for the given periodic function and…

Q: Problem 3 We assume y₁(x) solve the following differential equation: y" + P(x)y' + Q(x)y = 0, then…

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Q: Define P(n) to be the assertion that: What is the value of P(3)? n(n + 1)(2n + 1) 6

A: The assertion P(n) is defined as        ∑j=1nj2=n(n+1)(2n+1)6

Q: folve for Determinants using pivotal method B = 1 2 3 5 4 -1 7 8 4 4 7 2 4 34 4 G 5 7 6 2 1

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Q: A "swoosh" region is bounded by two quadratic polynomials. [Look up the Nike logo if you're…

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Q: 2. Consider the surface defined by 1² + 2xy + y² + 2²- 25 Let F(x, y, z) = 1² + 2xy + y² + 2². (a)…

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Q: Prove by induction that Σ₁₁ (5¹ + 4) = (5¹+¹ + 16n − 5) - i=1

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Q: Suppose f: R → R is defined by the property that f(x) = x cos(x) for every real number x, and g: R →…

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Q: QUESTION 2 You borrow $12,000 from your bank to help pay for some emergency home repairs. This loan…

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Q: (a) Set up the integral used to evaluate the line integral using a parametric description of C. Use…

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Q: Suppose f(x) = x + x² + x³ for every real number . True or false: The function f is strictly…

A: We are given        f(x) = x + x2 + x3  Differentiating w.r.t x, we get        f'(x) = 1 + 2x + 3x2…

Q: find the order of the given factor group.

A: The elements of the factor group (Z3 × Z6)/<(1, 2)> are of the form (a, b) + <(1, 2)>…

Q: : Given the following table find x3.fo.Af, A. 11 fo j 0 2 on xj 4 4 20 14 30 Af. 30 Af₁ Afz A²%.…

A: note : Since xi is an external variable, we can't find the value of x3 from the table as it must be…

Q: 3 to solve. His work is shown at the right. His 8) Ricardo was given the equation + ² = teacher told…

A: We see the actual equation was       3/x2 + 5/x = 1/2  Ricardo then multiplied the above equation by…

Q: What is the z transform of x(n) = 1, 0≤ n ≤ 5 a. z1+z²+z³ + 24 + z-5 b. z+1+z1+z²+z³+ z-4 1+z+z²+z³…

A: The Z-transform is a mathematical transformation used in digital signal processing to analyze and…

Q: Draw TWO different graphs each with 3 vertices having degrees 1, 2 and 3. Are these graphs the…

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Q: K Graph the constant-profit lines for the objective function P=x+y through (2,2) and also through…

A: The given objective function P=x+y through (2, 2) and (4, 4). To Find:  Graph the constant profit…

Q: A differential equation is given. Classify it as an ordinary differential equation (ODE) or a…

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Q: EXAMPLE 9 Solving a Homogeneous System of Linear Equations Solve the system of linear equations. x₁…

A: The given problem is to solve the given system of linear equations. Given system of linear equations…

Q: Solve the following initial value problem: 9y" - 6y + y = 1, y(0) = 4, y'(0) = -1.

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Q: Task: Do the indicated task individually. Apply the concepts you gained in this lesson in doing this…

A: Here are the given tasks, Using desmos graphing app, construct a curve and a line touching one of…

Q: tion Completion Status: Men Women Total French Toast 47 65 112 P(Men AND Pancakes) = 0.11 Find the…

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Q: That is, Use mathematical induction to prove that for all N ≥ 1: N k=1 k(k!) = (N+1)! - 1. 1(1!) +…

A: The given result ∑k=1Nkk!=N+1!-1. We have to prove this result using the mathematical induction.

Q: 619 3 + + 82 3e-5s 8 9 8-5 +7e-38 + + 2 s² +9 3 (8-2)4 1 8+3 + (s+3)2 + 25 (s + 2)² + 16

A: “Since you have posted a question with multiple sub parts, we willprovide the solution only to the…

Q: 7. Penguins huddle together to stay warm in very cold weather. Suppose that a certain type of pen-…

A: The diameter of each penguin is 14 inches.The diameter of the large circular cluster is 20 feet.

Q: 2. Use the method of Laplace transforms, as presented in the lecture, to solve the IVP with…

A: The given problem is to solve the given initial value problem with given initial conditions and then…

Q: The vector O True False 0 is a solution of the homogeneous system 3 1 -2 -12 10 | -4 8 70 0 0

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Q: what is the mean distance of these numbers 36,26,30,28

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Q: |y" + 3y + 2y = 1+ 8(t-1), y(0) = 1, y'(0) = -1

A: Introduction: In the given differential equation the Dirac delta function is occur. So, to find the…

Q: Let A and B be n-by-n matrices. Which of the following conditions is sufficient to conclude that…

A: A and B are n x n matrices.

Q: Prove that every planar graph must have a vertex of a degree less than 6.

A: We have to prove that: Every planar graph must have a vertex of a degree less than 6.

Q: 1 1 1 Given the matrix B= 1 1 1 1 1 1 Which of the following matrices solves X in the matrix…

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Q: Let R = {(a,, a,, a, ...)}, where each a; E Z. Let I = {(a,, a, az, ...)}, where only a finite…

A: Here given that R=a1, a2, a3......., where each ai∈Z. Consider, I=a1, a2, a3........ It has to be…

Q: 1. Carefully show all work and circle your answer. (a) Use l'Hospital's rule to find lim x sin(π/x).…

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Q: Exercise 12.3.5. Let A: V→ V be a linear map with eigen-pair: (r, A) E V x R. Prove the following:…

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Q: what is question e asking??

A: Question is asking that what combinations of investments and time we have to make at initially so…

Q: 1. Consider the following vectors in R³: (@ Which of the following equals |||||| + (7 · Ý)Z||? 7= 3…

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Q: Evaluate the integral by changing to spherical coordinates. 100 - x² 200- x² - y² 10 1. To 100000 3…

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Q: 1. Let B = 3 {B][F][C])}---E] and x = 3 -3 0 a. Show that both B is a bases for R² -8 3

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Q: 2. Given the equation above, find matrix A 0 23 14 34-9] A = 2

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Q: Use the properties of the definite integral to find ľ round. If it is not possible, write NP for…

A: We are given that           a∫b f(x)dx = 4           c∫b f(x)dx = -1     => a∫c f(x)dx = a∫b…

Q: The chord AB of the parabola y² = 4ax cuts the axis of the parabola at C. IfA = (at², 2at), B =…

A: Given that y2= 4ax is parabola and its chord cut the axis of parabola at a point C. and we have that…

Q: Consider the differential equation y' - y²x5-16.x". (a) Determine for which n the equation is…

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Q: Given the initial value problem f(x, y) = 2x² - y, y(0) = 2 and the step size 0.5, which is an…

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Q: Describe the set Span {u, v, 3u, 2u - 5v, 0} geometrically, where u = and v= 0

A: The set spanu, v, 3u, 2u-5v, 0, where u=101 and v=010. We have to describe the set geometrically.

Q: A golfer practices different parts of their game for hours. Specifically, the golfer practices: (1)…

A: Since you have posted 5 subparts of a question, as per the Bartleby answering guidelines we are here…