Complete the square of the quadratic function f(x) = 3x² - 18x + 26.

Q: The roots of the characteristic equation of a matrix represents the O of the matrix eigenvalues rank…

A: We will use basic definition of eigen values to conclude .

Q: Let F = Z₂ and let f(x) = x³ + x + 1 € F[x]. Suppose thataisa zero of f(x) in some extension of F.…

A: The given field is F=ℤ2 and the given polynomial is fx=x3+x+1∈Fx. (1) We know that a polynomial…

Q: Show that Lˆ is a linear operator, i.e., that is satisfies the necessary requirement for linear…

A: As per the question we are given a operator L̂ on the Hilbert space over ℂ [a, b] and we have to :…

Q: Consider a function space in (-∞0, ∞) with orthonormal basis {n}. Show that any function f(x)…

A: suppose that we express the function is the given format in the question -   f(x)= ∑n cnϕn^(x)⇒f(x)=…

Q: 1. Simplify the following :) [ (AUB) U (AUB')]' "1) (A²n B) U (Aºn B²)

A:

Q: (5-9)construct a Divided difference table for f(x) X². e-x/2 fi FIX,X1] 5).. 6)..... X₁ 1.1 2 3.5 5…

A:

Q: 4. (Parametrizations) (a) line segment from (5,-2, 10) to (-6,-4,1) Find parametric equations for…

A: Use the given information.

Q: Ifv+w= and v = [1]. C W= , compute and draw the vectors v and w.

A:

Q: (b) Consider the following, more general, true fact: For all n, m € Z\ {0} and g € N, if ged(n, m)…

A:

Q: Find an equation of the circle that has center (-5, -1) and passes through the origin.

A:

Q: Let z = 2i and w=3-i. Locate the numbers 2z+w, z-3w vectorially.

A:

Q: A. The integrating factor of zy' + 2y = is. B. 2 C. 13 D.

A: Given differential equation. xy'+2y=exx2 y'+2yx=exx3 Linear first order differential equation

Q: Given that U = {a, b, c, d, e, f, g, h, i, j, k, l, m} A = {a, b, c, f, l} B = {b, d, e, f, k, l, m}…

A:

Q: 1. y' + (x − x²)y' + y = 0, with y(0) = 2, y'(0) = −3.

A:

Q: The Dirac delta-function obeys: see image 1 a). Prove that: see image 1 b). see image 2 c). Now…

A: As per the question we are given the Dirac-delta function  δ(x) and we have to prove the following…

Q: A. x² = y² + 1 3. A. 4. ( 5. 3) The solution of = 5, y(1) = 1 is. B. y2 2+1 A. y cie + c₂e6 A. A. y…

A:

Q: A couple pays $600 at the end of each 6 months for 5 years into an ordinary annuity paying 6%…

A:

Q: Give an equation for the sphere with diameter PQ, where P = (1, 1,-5) and Q = (1,7,1). (Express…

A:

Q: Consider the statement, "Either -2 ≤ x ≤-1 or 1 ≤ x ≤ 2." The negation of this statement is Select…

A:

Q: Solve the following differential equation of separable variables. xy + 3x-y-3 xy - 2x + 4y - 8 dy dx…

A:

Q: Simpso (A) 587 (B) 400 8) Using three area segments between [0, 9], the estimated area under f(x)…

A:

Q: Nuclear power plants use Uranium-239 as a power source. U-239 has a half-life of about 2 years. a)…

A: Given the uranium isotope U-239 has a half life of about 2 years. (a) Given the chart for the amount…

Q: Find It and using this find the conditions on k that make Î self-adjoint.

A:

Q: lim I-X Calculate the following limits, or explain why they diverge. 3 sin r²- 6 cos(x/√2) x-6

A:

Q: 1. Solve the following linear programming model using simplex method. Maximize Subject to: z = 3x₁ +…

A:

Q: 5. Find the solution of the owing constrained maximizatio problems (assum y ≥ 0). (a) maxx,y {f(x,…

A: We find maximum value

Q: Find the image of (2,1,4), given the Linear transformation L(x,y,z)=(x+y, 2x,y+2z)

A: Lx,y,z=x+y,2x,y+2z Note: We are allowed to solve 1 question at a time

Q: Write an equation for the line through the point (1,3) parallel to the line y = x + 10.

A: The line passes through the point 1, 3 and parallel to the line y=12x+10. We have to find the…

Q: . Analyze algebraically what special case in simplex application is present in each of the LP model…

A:

Q: Let Z denote the set of positive integers. Define a relation R on Z+xZ+ by (m, n)R(s, t) iff gcd(m,…

A:

Q: 4. Find the maxima of the following functions (assume (a) f(x) = − x² – x4. ≥ 0).

A:

Q: Consider the matrix A defined as A = [1/2 1/2 1/2 1/2 0 0 0 1 a) Using the standard relations of the…

A:

Q: The zeroes of the function f(x) = a cos(1.5x) + √bx-c where a = 4, b = 2, and c = 3 can be…

A: fx=acos1.5x+bx-ca=4, b=2, c=3x0=6.13

Q: Which of the following is a linear transformation? T(x,y)=(3xy,2x+y) T(x,y)=(x+y+2,2x2)

A:

Q: Solve for r in terms of P, n, and t: P = (1 + ² )'

A:

Q: For each of the following functions decide whether it is injective, and whether it is surjective.…

A: Let, for a, b ∈ Q.               f(a) = f(b)            => 5 - a3 = 5 - b3            => a3 -…

Q: £x: be the method of Frobenius to find solns. of the 2x²y" + xy + (x²-3)y=0 (A) 4 0<x<e. in some…

A:

Q: In (Z13, +mod 13, mod 13 ), the multiplicative inverse of 7 is 3. Select one: O True O False

A:

Q: Solve for the particular solution: (D² - 2D + 6)y = 4e-2x O yp = (-1/2) e^(-2x) O yp = -2xe^(-2x) O…

A:

Q: Determine whether the function is a linear transformation. T: R² → R³, T(x, y) = (3x², 3xy, y²) O…

A: Given function  T:R²→R³, T(x, y) = (3x², 3xy, y²)

Q: √-1, are Show that the set of functions on(x) = exp(inx)/√2, where I and i = orthonormal in [—^, π]…

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

Q: 3. Make up a differential equation of the form dy/dt = f(t, y) that has y(t) = e² as a solution.…

A:

Q: The eigenvalue k and the eigenvector v of the matrix A follows: O O O O Av=kv insufficient…

A:

Q: 3 Calculate L{sin(5x)}

A: Lsin5t

Q: 16 + 25 =1 center: vertices: co-vertices: foci:

A: General formula for the Ellipse is  x-h2a2+y-k2b2=1 when a&lt;b, its major axis is along the y-axis…

Q: Let A and B be sets. The symmetric difference of A and B is Select one: a. (A − B) n (B − A) - - O…

A: Given: Two sets A and B. We have to write the symmetric difference of A and B.

Q: ay Problem 3: Given = (x+y-1), y(0) = 1, defined over the interval (0, 3] with a step h-1. Answer…

A:

Q: 28. Logzdz, where y(t) = eit, − ³7 ≤ t ≤ 37.

A:

Q: Oa. Every infinite subset of Ris countable.

A:

Q: (t-7)y' + (t-1)y = Int+t-¹, y(-2) = 4 Find the interval in which the solution of the initial value…

A: From the Existence Theorem : An ODE of the form y'+P(t)y=Q(t) has a solution in an interval, where…