Problem 3. Find an orthogonal diagonalization of the matrix A of Problem 1.

Q: Find the solution of the initial value problem Y' = AY, Y(0) = [1, 2] if we know that A has…

A:

Q: If n(C) = 34, n(C∩D) = 17, and n(C∪D) = 93, find n(D). n(D) =

A: The set A∪B contains all the elements that are present either in set A or in set B. It is known that…

Q: of the following statements is/are true! piz (A) For a nonzero matrix A E Rx, let P be a matrix that…

A:

Q: Consider the partial differential equation 8²u Du 8x² It' with boundary conditions u(0, t) = 0 and…

A:

Q: 6. S csch (In z) + coth (In z)csch (In z) z coth² (In z) dz

A:

Q: C. Solve the IVP. Indicate the method used. Show the details of your work. y+y = y³ y(0) =

A: Sol

Q: (1) Prove that the product xy of two real numbers x and y is nonnegative if and only if the absolute…

A: This is the problem of counting.

Q: 4- Which of the following is a Hamiltonian system? (a) x = y² - x, y = x, (c) i = y +3x, j=y,…

A:

Q: 17. How many edges has each of the complete bipartite graph K5,13? A. 65 B. 75 C. 55 D. 45

A:

Q: (1) Consider the following observation model b₁=₁+13+ b₂ = 12-213+n₂ b3 = 21-423 +723 b₁ = 21+223…

A:

Q: Using the method of undetermined coefficients, setup the form of the particular solution of the…

A:

Q: A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 1 gram…

A:

Q: Find the sum of the given vectors and illustrate geometrically. 12. (1, 3, -2), (0, 0, 6)

A: Now the two given vectors be <1,3,-2> and <0,0,6> . To find the sum of the given vectors…

Q: Let R[r], be a linear space with all polynomials p(x) = az²+bx+c (a,b,c ER) whose degree is no more…

A: We have to find the matrix A representing L with respect to the given basis. Then we can proceed…

Q: At the center of the lobby of a hotel is an artificial pond in the shape of an octagon serving as an…

A: Since the distance between consecutive spouts is 1.5 meters, then the length of each edge of the…

Q: The procedure to find the stationary points of a particular function f(x, y) leads to the eq 3x²…

A:

Q: Q- show that yo+(?) sy + (2) B²y_₁ = y + (1) DY...+ (1²¹) Ay -

A:

Q: Suppose that T: R4 → R³ is a linear transformation and that 5 T (1)-0(B)-0 T 2 2 5 Compute T (1 0 -3…

A:

Q: Fourier series fixis = x sinx ,xe (…,7)

A: The given problem is to find the Fourier series expansion of the given periodic function with given…

Q: y = 8/x , y = 2x ,X=4 O 6.355 sq. units O 6.455 sq. units O 6.555 sq. units O 6.655 sq. units оо

A: Let us consider the curve y=f(x) and y=g(x) The area under the region bounded  by the curve in the…

Q: What are the coordinates?

A: To answer the above question, suppose that the horizontal bold line represents the x-axis and the…

Q: Prove the following using either direct proof, indirect proof, or proof by contradiction. 1. If n…

A:

Q: 3. Find the inverse Laplace transform of (5s² + 4)/(s4 + 4s²)

A:

Q: A vector field is defined in spherical coordinates by F(r, 0,4)= r² cose, + r sin sine. Enter an…

A:

Q: Let f be an entire function. Show that (1) if Imf(z) ≥ 1, then f is a constant function. (2) if…

A:

Q: Show that the differential equation x³y² + x(1+yº)y′ = 0 is not exact, but becomes exact when…

A: We have to find the general solution to the differential equation x6y7+x1+y6y'=0

Q: please do this typewritten and completely so I will upvote. Thank you and much appreciated for the…

A: Given the radius increases at the rate of 16cm/ s ie., dr/dt =16 cm/s We have to find dA/dt when r=4…

Q: Evaluate: 0 xsinx 1 + x² dx

A:

Q: • 2π 0 rieit 20 + reit dt

A: The given integral is                               ∫02πrieitz0+reitdt

Q: 5. Consider the sequence {a} defined recursively as: a = 0, a₁ = 1, an = an-1 + an-2. Prove by…

A:

Q: The equation k₁ d³y k3 dx³ 4 dy ka (de) + k₂y - k5x³ = 0 where ki R, is a third-order homogeneous…

A:

Q: Nx - My M If = Q, where is a function of y only, then the differential equation M + Ny 0 has an…

A: Sol

Q: The perimeter of an equilateral triangle is (6x - 6.3 ) meters Draw and label a triangle to…

A: Sol

Q: 3 Let λ ER, and consider the vectors u, v, w E R³ defined by u = (3, 3, −6) v = (6, 7, -12) w = (3,…

A:

Q: 2. A cylindrical tank of radius 20 feet is being filled with water at the rate of 600 cubic feet per…

A: This is the question from the application of calculus.

Q: Example 5: Find the equation of the plane passing through the points (1, 2, -3), (2, 3, 1), and (0,…

A:

Q: For the following geometric sequence find a 14 3, 6, 12, 24…

A:

Q: The walls of a toilet, 2.5 m long, 2.05 m wide and 3 m high, are to be covered with tiles 15 cm by…

A: Since you have posted multiple questions and we can answer one question. So answered the first…

Q: 2. Find the duals. a) Maximize Z = 2x₁ + x2-x3 subject to: 2x1 + 2x2 ≤3 -X1 + 4x2 + 2x3 ≤ 5 X1, X2,…

A: Primal to dual conversion  Objective function is maximize  is converted to minimize Objective…

Q: Can this graph be traced? Use Euler’s theorem.

A: If a graph has an Euler circuit then it is traceable.  Now Euler's theorem says that If a graph has…

Q: cigarettes, 101 drank alcohol regularly and used illegal drugs, 106 smoked cigarettes and a used…

A: let number of students used alcohol daily be A number of students smoked regularly be S number of…

Q: 04-11 and det(A). mind the complex values. Calculate A²-24 +27. Calculate trace(4)

A: As per the policy, we allowed to solve only one question at a time. So I am answering the first…

Q: (a) If A₁ = {-i, -(i − 1), . . .−3,−2,−1, 0, 1, 2 }, for i = 1, 2, 3,. . . find (i) Un A6 and (ii)…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Test the convergence and divergence of the following series, find the sum of convergent series.…

A:

Q: Determine the multiplicity of 1 as a root of a polynomial f(x) = x³ 3x¹ +4x³ − 4x² + 3x − 1

A:

Q: 45. What is the connectivity (size of the smallest separating set) of the graph G? A. 3 B. 4 C. 5 D.…

A: Sol

Q: Assessment Evaluate each indefinite integral. 3. (8x³ + 6x²5x + 11) dx 2

A:

Q: x³ +1 Q3: Find the length of y=√x+2,1 ≤ x ≤ 7, Using ds = 1+²dy into the surface area of the object…

A: Find the arc length of y=x+2, 1≤x≤7 using the differential element ds=1+dxdy2dy. For formula for…

Q: if: x = t − 3, y = −1/2 t + 1 for −6 ≤t ≤6 is the equation. Can you: A) Graph the parametric…

A:

Q: Find parametric equations for the line described below. The line through the point P(2, 5, 0) and…

A: