Write down AT for the triangle graph. Find a vector y in its nullspace. The components of y are currents on the edges-how much current is going around the triangle?

Q: The sides of a triangle lie on the 3x+y-5-0, x-3y-1=0, and x+3y+7=0. Find the equation of the circle…

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Q: Show that $p_{k+1}<(b / a) p_{n}$

A: note : As per the most general case we will assume the transition equation to be : pk = apk-1 +…

Q: . The squares of a rectangular board of 11 rows and 9 columns are numbered sequentially 1 through 99…

A: We will discuss solution of given problems in next step.

Q: Find the splitting field for f (x) = (x2 + x + 2)(x2 + 2x + 2) over Z3[x]. Write f (x) as a product…

A: Given polynomial is: fx=x2+x+2x2+2x+2 To Find: The splitting field of fx over Z3x.Also, write fx as…

Q: Find a basis for and the dimension of the solution space of the homogeneous system of linear…

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Q: 1. If A is nonsingular then [adj(A)]-¹ = adj(A-¹). 2. The linear system AX = B has a solution if and…

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Q: Let α be a zero of x3 + x2 + 1 in some extension field of Z2. Find the multiplicative inverse of α +…

A: As per the question we are given a polynomial p(x) = x3 + x2 + 1 and α is a root of p(x) = 0 in some…

Q: Corollary - Let F be a field. Then F[x] is a unique factorization domain.

A: Given: Theorem 18.3: Every principal ideal domain is a unique factorization domain. Corollary: Let F…

Q: The Serie: n=1 sen (int) + i cos (int) nn We can affirm that it is: (a) is an absolutely convergent…

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Q: (a) Find the eigenvalues of the matrix of projection onto the plane x+2y+3z = 0 in R³. (b) Find the…

A: Note : As per our Guidelines we can solve first part as your part is not small. please repost…

Q: A diamond (see the figure below) is a quadrilateral with four sides of equal length. Its diagonals…

A: As per the question we are given a diamond shape which is a quadrilateral with four sides of equal…

Q: prove that each wff is a valid argument. (∀x)P(x) ^ (∃x)[P(x)]′ → (∃x)Q(x)

A: As per the question we have to prove that the following wff is a valid argument : (∀x)P(x) ^…

Q: 3) The vertical displacement From its natural length of a spring mass system is described by y" (t)…

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Q: Let A be a 4 x 4 matrix. Present systematically all cases for the Jordan Canonical Form of A.

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Q: Ans. Y t 44. Y+tY' - Y = 0, Y(0) = 0, Y'(0) = 1. 45. tY"+(1-2t)Y' - 2Y = 0, Y(0) = 1, Y'(0) = 2.…

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Q: Without using the Primitive Element Theorem, prove that if [K:F]is prime, then K has a primitive…

A: As per the question we have to show that if [K:F] is prime then K has a primitive element, without…

Q: Let f [a, b] → R be a bounded function. Then for any two partitions P₁, P₂ we have: : L(P₁, f) <…

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Q: (i)Suppose that g(x) = 1 + √x and f(g(x)) = 3+2√x+x, then find the function f(x) and (ii) let us…

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Q: mathematics

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Q: II. Is the matrix B = [100] 1 502 3 0 € M3 (R) diagonalizable? Justify your answer.

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Q: Calculate the compound amount. Use the compound amount formula and a calculator. (Round your answer…

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Q: The demand function of a monopolist's product is p = √600 – 2q. a. How many units should be produced…

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Q: Consider R³ together with the standard inner product. Transform the basis {(1, 1, 1), (0, 1, 1),…

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Q: The functions 1, cos x, sin x, cos 2x, sin 2x, ... are a basis for Hilbert space. Write the…

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Q: Problem 1 space? Which of the following sets is/are real linear vector O(A) {a+b√2} where a, b are…

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Q: (Every independent set is contained in a basis.) Let V be a finitedimensionalvector space and let…

A: To Show: If v1,v2,...,vn is a linearly independent set then there are vectors w1,w2,...,wm such that…

Q: Determine a Green function for the equation x²y"(x) + 2xy'(x)-2y(x) = f(x), with boundary conditions…

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Q: .Find the complete set of value of a such that (x^2-x)/(1-ax) attains all real values. b.Let the…

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Q: 1. Let V be an n-dimensional inner product space and let {u₁, 2,. for V. If v=au, and w= bu, where…

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Q: A dietician is planning a snack package of fruit and nuts. Each ounce of fruit will supply zero…

A: As per the question a dietician is creating a snack package that must meet certain nutritional…

Q: Let f(x)=e^(6x)-kx, for k>0 Using a calculator or computer, sketch the graph of f for k=1/9, 1/6,…

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Q: 2. Assume that f(x) is periodic with period 27 and, for <<, is given by the formula f(x) N 0 if 24…

A: The given problem is to sketch the given periodic function for -3π to 3π and also to find the…

Q: Choose a different cost vector c so the Ph.D. gets the job. Rewrite the dual problem (maximum income…

A: let's first understand the context of the problem. It sounds like there is a situation where a Ph.D.…

Q: +20x-22y-14-0 become when referred to the rectangul axes through the point (-2, -3), the new axes…

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Q: Let a be a complex zero of x2 + x + 1 over Q. Prove thatQ(√a) = Q(a).

A: As per the question we are given the polynomial  f(x) = x2 + x + 1 over the field of rational…

Q: In the notation of Example 7, show that d(xy) = d(x)d(y).

A: The function d is defined as, da+bi=a2+b2 To Prove: dxy=dxdy.

Q: Given a compact set A and a closed set B. ShOw that AB is compact!

A: Given Data: Let us consider the given data, A is a compact set B is closed. To show that : A∩B is…

Q: (a) Let T: VW be a linear transformation defined on vector spaces from V to W. If T(v₁),T(v₂),,T(v)…

A: Since you have posted multiple questions, we will provide the solution only to the first question…

Q: [an] 2. If A is similar to a diagonal matrix D then A is similar to AT.

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Q: Which of these functions from C[0, 1] to R (with the usual metric) are continuous?

A: Given: Functions are defined from C0, 1 to R. To find whether the following functions are…

Q: Let F = Z2 and let f (x) = x3 + x + 1 ∈ F[x]. Suppose that a is azero of f (x) in some extension of…

A: Given: F=ℤ2 and a is a zero of the polynomial fx=x3+x+1. We have to: (i) Find number of elements in…

Q: ven P(B) = 0.38, P(A and B) = 0.26, P(A or B) = 0.45, what is P(A)? Answer in decimal form.  Round…

A: We are given PB=0.38PA∩B=0.26PA∪B=0.45PA=?

Q: The projection of a vector on a plane Let P be a plane in space and let v be a vector. The vector…

A: Given: If P is the plane x+2y+6z=6 and v=i+j+k. To Find: projpv.

Q: Let Aij be a submatrix of a sudoku matrix A. Show that if λ is an eigenvalue of Aij, then |λ| ≤ 22.

A: As per the question we are given a square submatrix Aij of a sudoku matrix A. And we have to show…

Q: lim f (x) Show x→1 there isn't any.

A: Given,         f(x)=x2,x≥10x&lt;1.

Q: Straight lines passing through a fixed point (h, k). Parabolas with axis parallel to the x-axis.

A: We have to find the differential equation of the given families of curves.

Q: Problem 1. Let H be a Hilbert space and T: H → H be a linear application. Suppose that (Tx, x) > 0…

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Q: Given P(A) = 0.42, P(B) = 0.46, P(A or B) = 0.33, what is P(A and B)? Answer in decimal form.…

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Q: If Q and U are unitary matrices, show that Q-1 is unitary and also QU is unitary. Start from QHQ = f…

A: As per the question we are given two unitary matrices Q, U and we have to show that Q-1 , QU are…

Q: At what point should the origin be shifted if the coordinates of a point (4, 5) become (−3, 9)? The…

A: a

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.