1. Prove that i = (0, 1, 1), 2 = (1,0, 1) and üz = (1, 1,0) form a basis of R. 2. Find the components of w = (1, 1, 1) in the basis {1, 2, 3}

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A: This is a problem of multi-variable calculus.

Q: 7. Find the minimum of, f (x1, x2) = 2xỉ – x1x2 + 2x3 + x3 – 2x1x3 - And check the second order cond...

A: Given f(x1, x2 ,x3 ) = 2 x12  - x1 x2 + 2 x22 + x32 - 2 x1 x3for critical points put fx1  ,  fx2 ,  ...

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A: Greatest common factor  of a and b is a number that is the largest common factor of each of a and bo...

Q: 1 Consider the series >) 2 n(1+ ln? n) n=1

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Q: The vertices of ADEF are D(2, 5), E(6,3), and F(4,0). Graph ADEF and its image when you translate AD...

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Q: If L(x, y, y') = S 2y(1+ (y/)²)-'dæ what alternative form can the Euler equation Ly – Ly = 0 take? d...

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Q: e 4. Solve: y" – 2y'+y=- t

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Q: 16x? 36y? = 1

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Q: a. (6– j2)* b. (256/340°) (2562340")

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Q: Find the solution to the following initial value problem by finding the general solution to the diff...

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Q: (a) Put the system a" + y' – 2y = 1, x" + y' – x – y = 2 in operator matrix form. (b) Use the operat...

A: This is a problem of the system of the differential equations.

Q: (a) Let A € R™×n be a tridiagonal matrix, i.e. bị Ci ... az b2 c2 0 a3 b3 ... ... A = 0 0 0 0 0 0 bn...

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Q: dx Jatx)(xtan-"(x) + 1) -= In(F(x))+C. F(/3) if C=0? For What is F ( (xtan-1(x) + 1)

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Q: Determine the Laplace transform of: (a) cos(st + 0) (b) sin(ot + 0)

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Q: I Find the second derivative(y") of the following functions and simplify the final results. 1. y = x...

A: Some of the properties of derivative ddx(uv)=udvdx+vdudx ddxxn=nxn-1 ddx[af(x)+bg(x)]=addx(f(x))+bd...

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Q: Evaluate the Laplace transform of the following: cos kt} = sta 1. Prove: L{e-at 2. f(t) = e-3t(1+ si...

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Q: Find (∂z)/(∂s) and (∂z)/(∂t), given: (a) z = x2 - 2y2 ; x = 3s + 2t, y = 3s - 2t

A: It is given that,            z = x2-2y2  ;  x = 3s+2t  ;   y = 3s-2t We have to find  ∂z∂s  and  ∂z∂...

Q: 37. Which of the following accurately shows the constraint on the daily capacity for the third produ...

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Q: Identify whether each of the following is a polynomial function. Justify your answers. a) h(x) 2- Vi...

A: We have to choose polynomial function for given function.

Q: 2y + 5z - 3w = 16 2x + 3y + 3z + 4w = 110 2x + 5y -3z + 4w = 74 -x+ 4y + 5z - 2w = 30

A: We will reduce the system in echelon form by using row operations.

Q: Problem 8. Show that if the linear system Ax = b has more than one solution, then it must have infin...

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Q: A. Use the tabular method to evaluate the following limits. Set three values of x from each side. Ro...

A: Let f(x) = log(4-x2)cos(x)

Q: a) Find the length of the curve y(x) = x3/2/3- x/2, 3 < x < 4. b) Find the area of the surface obtai...

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Q: Let x, y ∈ Z. Prove that x − y is even if and only x and y are of the same parity.

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from ...

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Q: A man travels in a motorized boat at the rate of 12 kph from his barrio to the town and come back to...

A: The equation that describes the relation between the distance, rate, and time is Rate=DistanceTime.

Q: Find the vector component of v = 2i – j + 3k along b = 6i + 6j + 7k and the vector component of v or...

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Q: Solve for the general solution of equation (4), d²X + B²X(x) = 0 dx? Express the general solution in...

A: This is a problem of IV. 

Q: Can 199 cannot be written as the sum of an even integer and two odd integers. Show prove too.

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Q: F (x. y) = 3x²+3y² –18y+15 4- /2x+4y+4 a) Find domain b) Draw sign Diagram

A: The given function is Fx,y=3x2+3y2-18y+154-2x+4y+4. (a). We know that the domain of a function Fx,y=...

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A: As per Bartleby guidelines we're supported to answer only one question when two or more questions ar...

Q: Find the local maxima, local minima, and saddle points of = f (x, y) = x² + y + 2xy Identify x,y,and...

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Q: Find the maximum value of f(x,y,z)=y-z subject to x+y+z=1, x^2+y^2=1.

A: Let us consider the function f(x,y,z)  To determine the maxima subjected to g(x,y,z)=0 Find the lan...

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Q: Q1) Determine the gradient of the following scalar field V = e(2x+3y)cos5z Q2) Given f = x²y + 3z + ...

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

Q: Q3. For A= [56, 66, 72, 19, 54, 23, 23, 21, 65, 88] B= [30, 93, 21, 31, 36, 29, 56, 48, 33, 59] Plea...

A: Given  A=[56,66,72,19,54,23,23,21,65,88] B=[30,93,21,31,36,29,56,48,33,59]

Q: Question 10 Which of the following is the constant term in the expansion of (2z++) is O 160 / 27 O 8...

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Q: Problem 7. Prove that if A is symmetric and nonsingular, then A- is symmetric.

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Q: Solve: (cos x) · (dy/dx) + y sin x = 2x cos2 x, y(Tt/4) = (-15/2-n2)/32.

A: The given differential equation can be written as :            dydx +ytanx = 2xcosx So, the integrat...

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Q: Solve the linear system using Gauss-Jordan Method 2y + 5z - 3w = 16 2x + 3y + 3z + 4w = 110 2x + 5y ...

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Q: 7. The table below gives the power consumption in megawatts (MW) in San Diego County from midnight t...

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Q: Evaluate - (~ p < q) ^ ~ (p →~ q). O FFFT O FTTF O Tautology O FTFF O FFTF O Self-contradiction

A: As per our company guidelines we are supposed to answer only the first question. Kindly re Post the ...

Q: Given the orthogonal basis B for R4 and the vector v below, find the Fourier coefficients for v with...

A: Given  we have given the orthogonal basis for R4 and the vector v below  B =1-21-2, 10-10, 4-347, -2...

Q: 1- Solve the set of simultaneous equations below: a- 2x-4y=-24 9x-3y=-3 b- 2x+3y=27 6x+9y=81

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Q: Find the equation of the tangent plane Pr to the surface S:x2 +y? + z2 = 9 at (2,-1, 2)

A:  To find :Equation of tangent plane to the surface x2+y2+z2=9 at the point (2,-1,2).