Given the d. subspace V={(x,y,z)=R³ | 2x+y-z=0} of the d. space (R³(R),+,-) and the vector =(3,-5,1)=R³. ind a basis B₁ of V and then prove that the set B2 ={(-1,3,1),(-1,4,2)} is also a basis of V, 1#B2. Give the coordinates of the vector u to the base B₁

Q: a.) 4xy" + 3x³y'-7x = sin(2x)e²x b.) 5xy+3 dy dx = 2e¹¹

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Q: Show that set : A = {(x,y) = R² : sin(x) ≤ y ≤ 2e-2²] is closed on Euclidean plane R².

A: The given set is: A=x,y∈ℝ2: sinx≤y≤2e-x2. We need to shoe that the set A is closed in Euclidean…

Q: Modulo Rules. Find the remainders a = 222; b = 13 Answer 1310

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Q: Suppose U(x, y, z) = xy² z³ is the utility function of a person consuming x, y and z units of three…

A: Given: U(x,y,z)=xy2z3   Lagrange multiplier method: The Lagrange multiplier method is a mathematical…

Q: Given the parametric curve r (t)=⟨sin(πt),t⟩ where −1≤t≤1, find r ′ (t) and sketch the curve,…

A: A tangent vector is defined as it shows the direction of the motion. The tangent vector is found by…

Q: Let U = {1,2,3,4,5), A = {1,3,5}, B = {1,3,4), and C = {2,3,5). (a) Find A U (BUC). (b) Find (AUB)…

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Q: Prove that Z ⨁ Z is not cyclic. Does your proof work for Z ⨁ Gwhere G is any group with more than…

A: To Do: Z⊕Z is not cyclic. Does the proof work for Z⊕G where G is any group with more than one…

Q: Solve the given initial-value problem. y(x) = - 4y" – 4y' – 3y = 0, y(0) = 1, y′(0) = 7 - 11 He (5)…

A: The given initial value problem is 4y''-4y'-3y=0. Here initial conditions are y0=1 and y'0=7. To…

Q: 2 proofs of binomial identities applied to Pell-Lucas numbers.

A: The Pell-Lucas numbers are a sequence of integers defined by the recurrence relation: P(n) = 2P(n-1)…

Q: 2. For each of the following transfer functions, write the corresponding differential equation a.)…

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Q: (Schr¨oder–Bernstein Theorem). Assume there exists a1–1 function f : X → Y and another 1–1 function…

A: Given: The existence of 1-1 functions f: X→Y and g: Y→X To prove: X~Y

Q: a.) 4xy" +3x³y'-7x = sin(2x)e²x dy dx b.) 5xy+3 = 2e¹¹ N

A: A differential equation is said to be linear if  (1) every dependent variable (i.e y) and every…

Q: Suppose f(x) = 8 - x². (a) Find the slope of the tangent line to the graph y = f(x) when x = −1. - f…

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Q: Find the general solution for the following differential equation: 3x²1 - 2xy + (−x² + 15y² + 2)y' =…

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Q: 5. Let X be the space of reals with the topology T = {X, [0, 1], 0) (Example 2.1(b)), and let A =…

A: The given topology is T=X,0,1,∅. The given sets are A=-1,1, B=2,3.   The derived set is the set of…

Q: Solve the partial differential equation      (D^2-DD'-2D'^2)z=x^3 Where D=z_x  , D'= z_y

A: Given partial differential equation is                     D2-DD'-2D'2z=x3   where   D≡∂z∂x  and…

Q: Giving f(0.23) = 0.362, f(0.53) = 0.143, f(0.86) = −1.143, please use inverse interpolating method…

A: Given that f0.23=0.362, f0.53=0.143, f0.86=-1.143. Using inverse interpolating method to get the…

Q: Consider the graph G: Determine whether the following graph has (3.1) an Euler trail. Explain. (3.2)…

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Q: (2) GIVEN: The three points in R³: B C = A = (1,0,1) (1,2,1) (1,1,– 2) FIND: a) the measure of ZACB,…

A: Given three points in R3 are         A = 1, 0, 1  ,   B = 1, -2, 1   ,  C =  1, 1, -2…

Q: 4-1) describe the possible echelon forms of the matrix. (a) A is a 3x3 matrix with linearly…

A: Given: In this question, the given details are, 4-1) Here, to describe the possible echelon forms of…

Q: 4. Let U, V be subsets of a metric space X and V be open. Show that if UnV = 0, then clUnV = 0.

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Q: If then A-1 Given b X = [3] I solve Ax - b. B A = -9 -5

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Q: Sketch the graph of a function that satisfies all of the given conditions. • f'(2) = f'(-2) = 0…

A: We have to draw the graph of the function which satisfied all the conditions given below. i.…

Q: 1. If x[n] is given below, sketch the functions listed. a. x[n+4] b. x[3-n] c. x[n]u[n] d.…

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Q: 4(x – 4) = 3(2x + 1) + 2     Solve for x  3                     5

A: The equation is defined as a mathematical expression that is made from two expressions and they are…

Q: d. Set up a definite integral whose value is the exact volume of the solid of revolution generated…

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Q: Determine the Laplace transform of the ODE: y' (t) = 6y' (t)- 4y (t) + 6x (t)

A: Given: Ordinary differential equation : y"t=6y't-4yt+6xtTo find: The Laplace transform of given…

Q: Exercise 6 Find a (real) general solution. Show each step of your w y" + 3y + 2y = 12x²

A: We will find general solution.

Q: 1) a = 7¹5, b = 5 715 =57×(7²)7 57 × 49 7 =57x47 =57x4x (4 2)³ 7×4 × 16 3 5 57×4×1 528 53 powers…

A: We have given that a=715  and b=5

Q: determine the Laplace transform of the following: f(t)=t+u(t) s+1 OF (s) = 5+¹ OF (s) == OF (s) =…

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Q: Obtain the power series solution of the following ODE near x = 0. 2xy^"+(1-2x^2)y^' -4xy=0

A: Sol:- We can start by assuming a power series solution of the form: y(x) = a0 + a1 x + a2 x2 + a3 x3…

Q: A line 4x+y=1 through the point A(2,-7) meets the line BC whose equation is 3x-4y+1=0 at the point…

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Q: 3x + 2y ≤ 6 3x - 2y ≥ 6 -y≥ 2

A: Given the inequality; 3x+2y≤6                13x-2y≥6                2       -y≥2                3…

Q: a. Show that n(t)= -g'(t)i + f'(t)j and - n(t)=g'(t)i-f'(t)j are both normal to the curve r(t)=f(t)i…

A: c)  the  given curve is r(t)=4- 81t2  i + 9t j  compare it with the form r(t)=f(t) i+g(t)j  we see…

Q: educe the line 2x-3y+5=0 in slope intercept,intercept,and normal forms.

A: We have             y=2x3+53≡mx+c  ←Genernal Equation of line  tanθ=m=23,c=53

Q: 5. Give an example of a family {Un new} of open subsets of R, with usual metric, such that new Un is…

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Q: Move the slider h so that the graph of y= f(x) in the answer box = x² gets shifted to the right 3…

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Q: The rate at which a body cools also depends on its exposed surface area S. If S is a constant, then…

A: The Rate at which a body cools down is given by, dTdt=kST-Tm where k < 0 and Tm is a constant.…

Q: C. Solve the initial value problem of the following DE using Laplace Transform. b.) y"" - 3y" = te³t…

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Q: b. Identify the systems from task (2a) that demonstrate closure, i.e., the result of the operation…

A: b) in the answer provided, we see the systems S1 and S3 satisfy the closure property.      For…

Q: Find the Midpoint M of the line segment joining the points Q=(-6,5) and D=(0,-3)

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Q: Select the option that gives a list of the stationary points of the function:  f (x,y) = x3 + 3x2 -…

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Q: Consider the following differential equation. (2x - 1) dx + (7y + 5) dy = 0 Let M = 2x - 1 and N =…

A: Let M=2x-1 and N=7y+5   My=∂M∂y=0Nx=∂N∂x=0 Here My = Nx hence the given equation is EXACT…

Q: In the following linear system, x+2y+ 7z = 5 x+3y+ 9z = 7 x+2y+ (a2+3)z = a+7 determine all…

A: Sol:- To determine the values of a for which the linear system has no solution, a unique solution,…

Q: Note: NOT WRONSKIAN 9 Use variation of parameters. (D²+1) y = sec ² x

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Q: 2. Prove the following: For any simple graph G = (V. E), V can be partitioned into X, Y, Z such that…

A: The objective is to prove that for any simple graph G=V,E, EX,Y,Z≥2E3. A simple graph is a graph…

Q: a. Reduce the line 2x-3y+5=0 in slope intercept,intercept,and normal forms. b.Find the equation of…

A: The slope-intercept form is y=mx+c where m is the slope and c is the intercept. which is the…

Q: decide if the given statement is true or false,and give a brief justification for your answer.If…

A: We have to prove that the given statement is true or not. L-1s+4s+42+9=e-4tcos3t.

Q: If H is a Hilbert space and SCH, show that S = S¹¹¹. When S is the same as S++ ? Justify.

A: Answer:If H is Hilbert space and SCH, show that S⊥=S⊥⊥⊥.when  S is same as S⊥⊥? Justfy.These…

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

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