Let A be a nxn square matrix having rank 2 then rank of (A^t A) is (A^t= Transpose of A)

Q: Consider the polar curves C1 : r =  4 + (3√2)/(2) cos θ and C2 : r = 2 − (√2)/(2)  cos θ as shown in…

A: There are two points of intersection.

Q: Lett: V→ V' be a linear transformation. Then (1) Ker (t) is a vector sub space of V, and (ii) im (1)…

A: The solution is given as

Q: The marginal cost of manufacturing a certain product is dC/dX = 17 + 0.005x .  If the cost of…

A: Solution

Q: 8). Prove the validity of the arguments using the method of conditional proof. a). p → q (qvr) → s…

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Q: Find the volume of the solid generated by the region bounded by y - x² = -3,x+y = 3 about y = -5.

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Q: please do part a and c only. The part c is the priority

A: As per the question we are given a surface S in xyz space as : 4y2 + 4z2 - x2 - 16 = 0 And we have…

Q: Identify and sketch the graph of the following SURFACES. 2 = √9-y²

A: We have z=9-y2 Since z is square root of 9-y2 so z is positive always. We can write z=9-y2 as:…

Q: . Show that the vectors V1=(0, 3, 1, -1); V2=(6, 0, 5, 1); V3=(4, -7, 1, 3) form a linearly…

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Q: Mondo furniture manufacturer, determines that in order to sell x tables, the price per table in…

A: The revenue function is calculated by multiplying the price function by the number of quantities.…

Q: || = 8, || = 3 and the angle between them is 125°. Determine |u-v|

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Q: 4) If V is the imaginary part of an analytic function f then an analytic function with real part vis…

A: Imaginary part of an analytic function is the harmonic conjugate of the real part of this fu5.

Q: Question 1: Show that X is Hausdorff if and only if the set S = {(x,x): x € X} is closed in X X X.…

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Q: III. Let S be the quadric with equation 4x² − (y - 3)² + 4z² = 4. a. What type of quadric is S? Find…

A: Let S be the quadric with equation    4x2 - (y-3)2 + 4z2 = 4 ⇒x2 - (y-3)2/4 + z2 =1

Q: Consider the polar curves C₁: r: = 3 (blue) and C₂:r = 2 − 2sin0 (red) and let R be the shaded…

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Q: 6) Let f(z)=(2²-z-1)7. If a²+a+1=0 and Im(a)>0, then find f(a). a) 128a b) -128g c) 128g² d) -128g²…

A: Note: As per our policy, we are allowed to answer only first part of question kindly post remaining…

Q: III. Let S be the quadric with equation 4x² − (y - 3)² + 4z² = 4. a. What type of quadric is S? Find…

A: Given,  S is the quadratic with equation 4x2 - (y-3)2 + 4 z2 = 4 Here S is a sphere  whose radius is…

Q: 2. Using both trapezoidal and Simpson rule, find the approximate values for the integral…

A: Here the lower limit is π4 and upper limit is π2

Q: (a) Solve the first order linear ordinary differential equation x sin x dy d.x + (sin x + x cos x) y…

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Q: find the polynomial f(x) for which x.f(x-1)=(x-3).f(x) prove that f(x)=x^2n + a^2n is not divisible…

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

Q: Let S be the surface with equation 4y2 + 4z²x² - 16 -0. 1. Find an equation of the trace of S on…

A: Solution:S be the surface with equation 4y2+4z2-x2-16=0⇒4y2+4z2-x2=161)Traces of S in the coordinate…

Q: 5. ) Write an equation for the graph of the rational function shown. Explain your reasoning. 5. 4 -8…

A: Given the graph is

Q: Q3: Use finite difference method to solve Laplace equation in the red domain illustrated below. Ax =…

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Q: n-dimensional rector space F. Prove that V is the vector space F, hence b

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Q: Given the matrices 1 3 A=[ B: 24 Find the matrix (AB)T 이유 이 이요 04 21 28 6 12 18 22 6 18 12 22 60…

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Q: u(x, y) and let f and g be twice differentiable functions. The al solution to the equation uy2r + 2y…

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Q: For the following problems, find the general solution. 129. y”+5y+y=x+e

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Q: (2) If c(z) ≥ 0 for all z = [0, 1], then a function minimizes J(v), that is, J(u) = inf J(v), with…

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Q: Solve the non-linear function using NR AND Secant Method. Use 5 decimal values and stop at & S…

A: Note : As per our policy, we are allowed to answer only first part of question kindly post remaining…

Q: What is a homomorphism in simplest terms? Also provide an example.

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Q: 5. D = 2000 2 1 -5 Evaluate D.

A: 2  0  0   0-5  3  0   0   3  2  4   0   4  2  1-5  =  (2)(-1)1+1 3  0   02  4   02  1-5…

Q: 2. Find the Fourier series of the given function f(x), which is assumed to have the period 2L. f(x)…

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Q: nonhomogeneous system tY' = 2-2 Y + -2t (₁-²₁).

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Q: Question 2: Show that path connectedness is topological property. Explain and show your work.

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Q: 3. Evaluate Iffa a x dV, S is the tetrahedron bounded by the S planes x+y+3z = 6, x = 0, y = 0 and 2…

A: We have the that S is bounded by the planes : x+y+3z=6x=0y=0z=0 So, from x+y+3z=6 we get z=6-x-y3…

Q: Using Pappus Theorem, find the volume formed by revolving about the x-axis the area bounded in the…

A: Given ,  Parabola be  x2 = 2py and 4py-p2-x2=0 4py-p2-x2=0x2 = 4py-p2x2 = 4py-p4 At intersectionx2…

Q: Find a set of parametric equations for the curve of intersection of the paraboloid x² + 4y² -z = 0…

A: Given curves are  x2+4y2-z=0    ......(1)2x-z=0              ......(2)

Q: Let S be the surface with equation 4y² + 4z²x² - 16 = 0. +4√3 1. Find an equation of the trace of S…

A: Solution

Q: 1. Find the inverse of A = 1 1 0 1] 1 2 3 1 1 using the Gauss-Jordan method.

A: Solution

Q: Consider the vector-valued function R(t) = 1. Find the domain of R. (₁ In(3-1), 4t-8,31²-8), (0,…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Let {f1, f2, f3} be the dual basis of {e1, €2, €3} for R³, where e₁ = (1, 1, 1), €₂=(1,1,−1), Find…

A: Given basis are e1,e2,e3 of R3 where e1=1,1,1e2=1,1,-1e3=1,-1,-1 Its dual basis are f1,f2,f3 We have…

Q: 36. Sin(xy) + cos(yz) = 1. Compute z and az at P = (2, п/12,4). дх ду

A: Let us consider the given function z=f(x,y) The partial derivative of the function is obtained as…

Q: Let C be the parametric curve defined by x(t) = t²-t-6, [y(t) = 4t³ + 3t² − 6t. a. Determine the…

A: Given: xt=t2-t-6yt=4t3+3t2-6t To find: a) Horizontal tangent line b) Definite integral

Q: 8. If Z is an (n−1)-dimensional subspace of an n-dimensional vector space X, show that Z is the null…

A: Given: n-1 dimensional subspace To find: Scalar multiple

Q: 10. Determine the value for k for which the two lines are parallel and the value for k for which the…

A: The given lines are       L1: x, y=3, 2+t4, -5   and      L2: x, y=1, 1+s7, k

Q: Compute the fifth roots of unity.

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Q: Find the solution to the system 2x-8y + 5z =-5 2x+y=z=12 -5x+3y+9z=-17 . using (a) Jacobi Iterative…

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Q: Consider the initial value problem u" + p(t)u' + q(t)u = g(t), u(0) = uo, u'(0) = u Transform this…

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Q: (k) The solution of the following problem for the heat equation with nonhomge- neous boundary…

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Q: 2. Using both trapezoidal and Simpson rule, find the approximate values for the integral…

A: Let  I= ∫π4π2ln(tanx)dx Here, a=π4 , b=π2 , f(x) =ln(tanx) Step size h=b-1n=π2-π410=π410=π40 Then…

Q: Let A be an n x n symmetric matrix, R be an n xm matrix such that with m ≤n), and let B = R¹ AR (an…

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