Consider the vector space generated by [0, 1, –1, –1], [1,0, 2, 4], [1, 2, –4, 0]. Find an orthogonal basis.

Q: Show the span {(1,0, 1), (-1, 2, 3), (0, 1, – 1)} is all of R'.

A: Let x=1, 0, 1, y=-1, 2, 3 and z=0, 1, -1. We have to show that spanx, y, z is actually the vector…

Q: Prove the following using the rule of replacement and rule of inference. Let C = set of all students…

A: This is a problem of Logic.

Q: Find the solution, (D3+3D2+3D+1)y = 0 A y = c,e*+ (c,x+czx²)e-* y = c,+c,e"+c;e¯ B C D y =…

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Q: 86s - 78 Find the Inverse Laplace Transform of +3)(s-4)(5s– 1) - 2e -+ 3e+e3 В 41 - 3e

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Q: b) Find the angle (0) between vectors between s = [1, –5, 4] and t = [3,3, 3].

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Q: For x, y, z, w > 0, prove that (x/z)+(y/z)+(z/w)+(w/x)≥4

A: It should by x/y, instead of x/z

Q: 6. Tell whether the series whose nth term is given below converges absolutely, condition- ally, or…

A: Please post the multiple parts separately. Here I answered 1st question as per our policy.

Q: Solve for the domain and range of. f(x.y,z) = 4-x2-y?

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Q: Show that the lines L:a =4- t, y = 2t, z =1+t and L2:2 =1+ 21, y = 3 – 4t, z = 5 – 2t are parallel…

A: This is a problem of 3D analytical geometry and application of calculus, vector calculus.

Q: What is the general solution to the differential equation (tan x)dy – (4y In y – y tan³x)sec²x dx =…

A: We will convert given differential equation into linear differential equation by appropriate…

Q: exercise Find the laplace of each f(t) 2. sin8t sin6t

A: We have to find the Laplace transform of ft=sin8tsin6t

Q: Identify and sketch the graph of the following equations in R. (a) r2+2y? + z2 – 8r + 12y - 2z + 35…

A: The given equation for part (a) is x2+2y2+z2-8x+12y-2z+35=0. The given equation for part (b) is…

Q: 1. In at most two sentences, address the following: • Give at least two postulates of Euclidean…

A: Postulate 1 A straight line segment can be drawn joining any two points.Postulate 2 Any straight…

Q: 9. Find all integers x, 0 < x < n, satisfying each of the fol- lowing congruences mod n. If no such…

A: Q (d),(g) asked and answered.

Q: 3. Given the parent function f(x) = |x|, write the equation of the function g(x) whose graph is…

A: The graph of a function f(x) is the ordered pair of points (x,y) in the cartesian coordinate system…

Q: For x,y E [0,1], prove that xy(1-x-y)≤1/27

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Q: A. Find the area enclosed by each of the following curves. T= 4 sin e

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Q: In the Laurent expansion of f(z) = valid in the region 1 < [z| < (:-1)(=-2) 2, the co-efficient of -…

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Q: Use the Newton Raphson Method to find the root of f(x) using 2.2 as the starting value of x. Iterate…

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Q: Evaluate the integral shown using Simpson's 1/3 Rule with 20 panels. 12 4arctan dx O 32.52059525 O…

A: Given integral is ∫2124arctanx6dx

Q: 34. (a) Find a parametric representation for the torus obtained by rotating about the z-axis the…

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Q: 2. Using Lagrange multipliers, find three positive numbers whose sum is 18 and such that the sum of…

A: Given, three positive numbers whose sum is 18 and such that the sum of their square is as small as…

Q: 1. Given a two variables function z = f(x, y) = V64 – 4x2 – y2. (i) Determine the domain and range…

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Q: 1. Given the series, A (2x-1)", find the radius and interval of convergence.

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Q: 7 similar cars are entered in a race. The cars all have an equal chance of winning and there are no…

A: Given 7 similar cars are entered in a race. To select 1st position ,7C1= 7 choices. To select 2nd…

Q: Using Bisection method find the solution of h (x): = xcos2x +1 = (x - 2)2. Use as initial values and…

A: given method hx=xcos2x+1=x-22 use as initial values π2 and 5π6. stop iteration if the error is less…

Q: Let A = [ 3*0 .8 = [ Jand C = [14-0 Jand c = [1* | Find the matrix X, if 8+0 -10 A? + 3X =C |B|

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Q: Q/Determine the Fourier series of the periodic function whose definitions in one period is? (4) Cos…

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Q: Part I. Cartesian Product and Relation Give the Relation: 1. Find a relation R such that >l if A =…

A: 1) The Relation R such that x+y2&gt;1 is  R={(0,3),(1,2),(1,3),(2,1),(2,2),(2,3)} 2) the Relation R…

Q: Find the solution. dy +y= dx 1+e* A y = ce¯*+e¯*In(1+e*) B В y = ce¯ – e ¯*In(1-e*) се © y =…

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Q: dy What is the general solution to the differential equation — 1 + бхе*-У? dx yey-x = x – 2 In(x +…

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Q: Find the solution dy y =Dxy dx

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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: Question 12 Consider the following IVP: y"+a?y = 0; y(0) = 1, y'(O) = 0 Find the general solution.…

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Q: What is the general solution to the differential equation sin y (x + sin y)dx + 2x² cos y dy = 0 ?…

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Q: y(5) - 8y(4) + 26y""– 48y" + 45y' = 0 (3) | a) Determine the characteristic equation o (m)=0…

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Q: Tabulate the differences of Euclidean, elliptic, and hyperbolic geometry according to the four…

A: Given: To find the difference between Euclidean Geometry, Elliptical Geometry, and hyperbolic…

Q: Se-2t if 0 3,

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Q: Solve the given system of linear equations using the Elimination Method. 4.)     2x1 + 7x2 + 15x3 =…

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Q: Question 2: A discrete random variable X has a probability distribution function given by P(X = x) =…

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Q: What is the general solution to the differential equation y - O + = dx? dx In(Ay – 2) = Ax + B y2 =…

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Q: Which of the following is the general solution to the differential equation (x + 2y)dx + (x + 2y +…

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Q: a. Write in your own words a definition of a complex numbers and Modulus of the complex number.…

A: This is a problem of complex analysis.

Q: Approximate the roots of the polynomial f(x) = X³ - 7X + 6 using False-position method.

A: We will find Approximate the roots of polynomial f(x) = x3-7x+6 using False-position method. steps…

Q: Find the Laplace Transform of h(t) = t? sin(2t) = ='s 3s2-4 A H(s) = (s2+4) 2 482 – 3 B H(s) =…

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Q: dy dx ytsinx I+ CoS X

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Q: Find the area of the shaded region. r = Vcos 20 r = 6 cos 0 NOTE: Enter the exact answer. A =

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Q: 2. Rate of calorie consumption. The table below shows the number of calories used per minute as a…

A: Given the table Activity  100lb 120lb 150lb 170lb 200lb 220lb walking 2.7 3.2 4 4.6 5.4 5.9…

Q: 1. Are the following matrices diagonalisable? Explain your answer. 2 0 50 1] a) A =-2 3 -1 -2 0 3 c)…

A: A matrix is diagonalizable if and only if for each eigenvalue the dimension of the eigenspace is…

Q: [2 - 3 2 – 3 and be express as A = LU as below L4 1 c) Let A = 1 1 2 [2 3 1 1 [U11 U12 U13 - 7 l21 1…

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