Q8: Given that -2 X = 1 8 -8 -9 -9,Z -7 7 -2. -8 5 what is the matrix 3X + Y – 3Z?

Q: 1- Use Euler Method to find value of y at x = 1.5 for the D.E. y' = x/y with initial value y(o) =…

A: We first find the solution by Euler method using the step size h=0.3 of the given differential…

Q: 1. Determine whether f is Riemann integrable over (0, 1] and evaluate S f(z) dr whenever fE R(0, 1])…

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Q: Prove that l17 is the only prime number of the form n²- 64.|

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Q: 2. (i) A square matrix A is called idempotent if A? = A. Find all 2 x 2 matrices A over the real…

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Q: 3. Two n xn matrices A, B are called similar if there exists an invertible n x n matrix S such that…

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Q: 4) The curver= V1 + sin20,

A: Solution :-

Q: Use the above formula to write each of the following limits as an integral (a) (b) Lm=0 nm-T lim n2…

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Q: Consider the vectors v, = (1 0) and v, = (0 1) in R,. the vector ( 0.4 3.7) can be written as a…

A: Linear combination

Q: Let V be the space spanned by f 1 = sin x and f2 = cos x. (a) Show that gi = 2sin x + cos x and g2 =…

A: Here we use the definition of basis of vector space is the smallest linearly independent set…

Q: In certain sampling inspection, the number of defectives found in 10 samples of 100 each are as…

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Q: distance between point Al2,4) Perpendicular on the line L:3y=3+X is solution:- 1) 149.3 2) 53,41 3)…

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Q: (b) Let X be a space and A ,B are subsets of X such that ACB and A closed, B open, show that X is…

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Q: Can you explain number 2? How did you know that is the formula to use?

A: Let V be a vector space over R  Define a function ·:V x V→ℝ Then the function is said to be inner…

Q: Consider the graph as shown in figure and determine the following: Pendant vertices, pendant edges,…

A: 1. Pendant vertices are d,e,f,g Pendant edges are ad edge,eb edge,fb edge,gb edge, Odd vertices are…

Q: Determine S[f] (Fourier series) if: a) f(x) = 2x; x ∈[-1, 1] such that f(x) = f(x+2)

A: *By Bartleby policy I have to solve only first one as these are all unrelated problems.These are all…

Q: Find the subspace generated by the vectors A= (2,1,-5), B= (4,3,7) %3D %3D So in space R³

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Q: a) Given the vectors in R3 v, =(11 -3), vz= (1 -3 1), v3=(-3 11) Using the system of linear…

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Q: d.x = -2x + 5Y dt dy -2.x + 4y dt 5 cost X = \ sin t et 3 cost –

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Q: · (D³ - 3D² - D + 3)y = 0

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Q: 3. Your marble collection has 125 red marble, 12 ae marblen, and I gen martien Is hw many ways can…

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Q: Consider the vector v = (5 1 -3) in R3. v belongs to Span{(2 -1 0), (1 2 -3)}. %D Select one: True O…

A: Spanning set

Q: Next, we must find the total distance traveled by the particle in the given time interval. This is…

A: To find the interval for which the velocity is negative and positive.

Q: Let E Os 0s n, 0s zs 1, 8Vzs rS 8. Compute

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Q: FOURIER SERIES Find the Fourier series of f(x) as given over one period. Sketch f(x). (Show the…

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Q: Consider the real sequence {an} given by an = ln(n + 1) − ln(n + 2), n ∈ Z≥0 = N ∪ {0}. Justify…

A: Given series is telescoping series  An infinite series to be convergent if its limit of the partial…

Q: 9. Consider the R region shown in the following figure, which involves the curves of equations: 22 +…

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Q: (b) Find the matrix representation [J]Bn+1,Bn• ght as Mon onas hUiver Unn mersi niversi ash ve

A: The given question is related with linear transformation. Let n ≥ 1 be an integer , and let J : Pn →…

Q: Give values for the Fourier sine series S(x) = ) Bn sin 00 (-) пт %3D 4 n-1 S(4) = S(-1) = S(7) =

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Q: +) Use the Euler methad's Salvetue:. C1 )りy=eッh=o.2

A: Euler's method

Q: 9. Solve the given (matrix) linear system: [1 0 X' = 1 5 L2 4 -3] 1 X %3D

A: Solution :-

Q: Let V = R be the set of positive real numbers. We define addition and multiplication with standard…

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Q: 3. Let n > 1 be an integer, and let J : Pn → Pn+1 be the indefinite integration transformation on…

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Q: (d) a sin 0 d0 + (x³ – 2x2 cos 0) dx = 0 - %3D (e) x dy - [y + xy°(1+ ln x)] dx = 0 %3D

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Q: Question 4. (or both) that is an equivalence relation, write the equivalence class of any one…

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Q: IV. Suppose z is a function of r and y, and tan y2 + x² = 2*e. Solve for az dz and %3D dy

A: To solve for dz/dy and dz/dx.

Q: If you are asked to apply Euler's method with (xo, yo) = (1, 7) and step size h = 0.5, how many…

A: As here given the initial condition (x0,y0)=(1,7) and h=0.5. And here we calculate for x=3 .…

Q: Find the volume of the solid generated when the plane region bounded by x = y? and x + y = 2 is…

A: To find the volume of the solid generated when the plane region bounded by  x=y2 and x+y=2 is…

Q: Show that if H and K are subgroups of an abelian group G then {hk: h element of H and k element of K…

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Q: (c) Let M be the surface with the equation r³ +y³ +z = 9 that is above the right triangular region…

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Q: 2. At what point on the line y = b does the line segment from (0,0) to ( a,0) subtend the greatest…

A: at what point on the line y=b does the line segment from 0,0 to a,0 subtend the greatest angle.

Q: How would you create a parallel line that passes through a given point using rotation?

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Q: 7,Prove the following fact: for any two positive integer a and b, gcd(2ª – 1, 2° – 1) = 29cd(a,b)–1.…

A: The question has a typo. It should be gcd(2^a -1, 2^b-1)=2^(gcd(a,b))-1. The -1 is not in the power.…

Q: For the given triple integral, which of the following is the transformed integral in the spherical…

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Q: Definition: The AREA A of the region S that lies under the graph of the continuous function f is the…

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Q: 1. Raul has a wall 4 units long and 2 units wide in the Cartesian plane centered on the origin. On…

A: 1st we will find point of intersection and then draw region bounded

Q: Consider the vector v = ( 5 1 -3) in R3. v belongs to Span{(2 -1 0), (1 2 -3)}. V | Select one: True…

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Q: The figure below to the left is a graph of f(x), and below to the right is g(x). 1.5 1.5 0.5 F0,5…

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Q: The combined SAT scores for the students at a local high school are normally distributed with a mean…

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Q: 1. Verify Green's theorem in the plane for $ (3x2- 8y,dx + (4y - 6xy)dy, where C is the boundary of…

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Q: 1. In how many ways can we distribute eight identical white balls into four distinct containers so…

A: Number of ways of distributing n identical balls into r distinct boxes =n+r-1r-1 Number of ways of…