Find a 3*3 symmetric matrox A so tht the characteristic polynomial of A is P(x) = x^2(3-x) and the null space of A is {k x1 x2 x3 : x1+x2-2x^3=0, k € C}

Q: If q(x) is an arbitrary polynomial in Pn it follows that                                      q(x) =…

A: Given, if q(x) is an arbitrary polynomial in Pn it follows that                   q(x) = c0p0(x) + .…

Q: 6) Given e>0 and fe (a) C(0,1) (b) C[-1,1] (e) a or b (d) C2m. There exist an algebraic polynomial P…

A: (Solving the first question as per our guidelines) Solution: We know that For each f∈C0,1 there is a…

Q: Show that f(x)=x\power{2}-3 is the minimal polynomial of \sqrt{3} over Q,

A: Let            We  have to  find the  minimal  polynomial of  the    over Let Then,  Suppose  that

Q: Which of the following monic quadratic polynomials is irreducible in ℤ_3[x]? Hint: f(x)=(x-a)(x-b)…

A:

Q: Consider the interpolating polynomial for f(x) = 15 with interpolation nodes x = 0, 2, 4, 6, 8, 10.…

A: The Interpolation Error: Suppose x0,x1,......xn are (n+1) distinct points in the interval [a,b] and…

Q: Find the polynomial p2 (z) = a0 +ajz+ azz? nat interpolates the ponts (0, -1). (2, –1) and (3,2).…

A: Let the polynomial be  p2(x)=a0+a1x+a2x2                                      (1) As equation (1)…

Q: Let f(x)= x³ + 2x+ 1 and g(x)= 4x + 1 be two polynomials in a ring (Zs[x],+ ,.). Find q(x) and r(x).

A:

Q: An operator whose minimal polynomial is different from its characteristic polynomial

A:

Q: The coordinates of the P(x)=x³ – 2x2 + 3x polynomial with respect to the base B-[1, x, x?,x'] are as…

A:

Q: Express K (x) in terms of the orthonormal Legendre's polynomials, with the inner product. Here, K(x)…

A:

Q: his is some (a) Use this

A: Given  (a) y" + 3y' + 2y = f(t), y(0)=y'(O)=0. (b)f(t) = e3t and f(t) = t.

Q: 3. Consider the following data set -2012 f(x₂) 5 1 -1 5 (a) Construct the quadratic Lagrange…

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

Q: Suppose P(z) is a polynomial satisfying • P(5) = - 5 P'(5) P"(5) = - 156 Р(3) (5) 3D — 414 305

A: Introduction: The term "polynomial" refers to a sort of expression. A mathematical statement without…

Q: (a) Let xo, ₁,..., n be n+1 distinct points in [a, b], with co= a and cn = b, and f € C+¹[a, b]. Let…

A:

Q: f(x) = y= Find the domain and the ring x 2 x+2 x² 2 3 / /

A: What is Domain and Range of a Function: A function always maps two sets. Either the two sets are…

Q: A function f satisfies the condition f(x+T)= -f(x) for all . Show that all its even Fourier…

A:

Q: P(x1, #2) –X2, Q(x1, x2) = x1; D = {(x1,x2) :0 < x1 < 1,0 < x2 < 1}. = -

A: Note : " As per our guidelines we will solve only first question . If you want any specific question…

Q: Find the wronskian of f1= x2-6x, f2=x2+6x, f3= x2-3

A:

Q: Write the Hermite interpolating polynomial satisfies |H(x₁) = Coo₂ | H (x₁) = C₁0 ₂ How to compute…

A: As per the question we have to find the Hermit interpolation polynomial H(x) for the given…

Q: This piecewise polynomial is NOT a cubic spline: if 0sx<1 if 1sx<2 %3D S(x) = So(x) = 6 S, (x) = 6+…

A:

Q: Consider the polynomials a(x) = r' + x³ + x + 4 and b(x) = 2r³ + 4.x² + x + 2 from Z5[r]. a) Find…

A:

Q: By using Ho (X) = 1 = 1 and HI (X)=2x in Hermit polynomials, calculate the value of Hg (1) ?

A: The Hermite polynomial is a particular set of orthogonal polynomials. According to the definition…

Q: 4) For Bernstein polynomial, B₁ (f; x) = Σk=o (k) x* (1 − x)"-kƒ (), we have B₁ (2t² + 1;x) = 2x² +…

A:

Q: When calculating the first Lagrange polynomial using x0, X1 we obtain L,(x) =x-3, then Xo and x, are…

A:

Q: Check if f (x) = 4x³ + 3x¹ − 12x² + 3 is irreducible in Q[r].

A: Note: As company policy, we solve only the first question. Please resubmit the rest of the questions…

Q: Show that the polynomial z5 + 14z + 2 has four zeros in the annulus </2 < 2.

A: Given

Q: Find a polynomial P(x) = x' + ax² + bx + c satisfying all the following properties 1) P(0) = 0 2) x…

A: Given form of polynomial,  P(x) = x3 + ax2 + bx + c To find the polynomial which follows below…

Q: which of the following monic quadratic polynomials is irreducible in Z_3[x]? note that : f(x) =…

A:

Q: The quadrature rule [“ f(x)dx = w₁ f(x1) + w2f(x2) + E (2) -h can be made exact for all cubic…

A: Given Information:The quadrature rule is given as .Objective:Write the four equations satisfied by…

Q: The first three Hermite polynomials are Ho(x) = 1, H₁(x) polynomials are defined using the inner…

A:

Q: Factor f(x) = x¹³ - x € Q[x] completely into irreducible factors. Hint: Factor out x first. The…

A:

Q: Suppose P(z)= ao+a₁z + a₂z²+ ... + anzn is a polynomial of degree n. Show that for each 0 k≤n, the…

A:

Q: How do I find the syndrome polynomial s(x) = w(x) mod g(x), where g(x) = 1+x+x^2+x^4+x^8 and w(x) =…

A: To find the syndrome polynomial s(x) given  and, we need to perform polynomial division w(x)÷g(x)…

Q: 11. The Hermite polynomials, H,„(x), satisfy the following: į. = Se-**H„(x)Hm(x) dx = \T2"n! 8,m:…

A: To prove: ∫-∞∞xe-x2HnxHmxdx=π2n-1n![δm,n-1+2n+1δm,n+1] Proof: Take the LHS ∫-∞∞xe-x2HnxHmxdx and…

Q: th integral coefficients tha D4, 3+i

A: The integer coefficient property is stated as If the polynomial with real coefficients , has a root…

Q: If f (2) and g(2) are monic polynomials of minimal degree for which A is a root then f(2)=g(2).

A: Given that f(λ) and g(λ) be the monic polynomials. the degree is minimum. and  given that the root…

Q: f(x) = x² − 3 is the minimal polynomial of √3 over Q,

A: We have that              f(x) = x2-3  be a polynomial of two degree.

Q: Find all irreducible polynomials in Z_2[x] of degree less than or equal to 3.

A:

Q: 12n+1) x Pa (x) : (n +1) Prte tx) +n Pane (x) a) Get the Le gendre reconnection polynomials using…

A:

Q: Find the wronskian of f1= x2-6x, f2=x2+6x, f3= x2-3

A: