14. The following vectors are the translation vector T and the spanning vectors X1 and X2, obtained by Gaussian elimination to solve a linear system of three equations in variables r, y, z, and w. T = X1 X2 (a) Which are the free variables? How can you tell?

Q: Suppose that the solution set of the homogeneous system Ax = 0 is given by the form X1 = -4r +5s, x2…

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Q: 2. An is a set of points (x, y) in a plane such that the sum of the distances between (x, y) and two…

A: We know that, The sum of distances to any point on the ellipse x,y from the two foci c,0 and -c,0 is…

Q: [] -3 -3 Let y = -9 uj -5 u2 5 Find the distance from y to the plane in R3 spanned by ul and u2.

A: Consider the provided question,

Q: 4. For the linear canonical system x' = Jx, x € R², determine the nature of the origin as a fixed…

A: Given canonical system x'= Jx  Case-1:-  det >0 if both Eigen value positive:- The product of the…

Q: 5. Show that the vectors a = 3i- j+4k, b = i- 3j – 2k and c = 4i – 3j+2k are linearly independent.…

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Q: Suppose that Mrs. Jena (in the position of T) want to travel to the top of regions diagonally right…

A: To find the number of route to reach the top of the region :-

Q: 6. Consider the vectors u = (1,–2), v = (4,3), and w = (9,4). Find scalars k and k2 such that w =…

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Q: 7 Prove or give a counterexample: If v1, V2, . . . , Vm is a linearly indepen- dent list of vectors…

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Q: i. Start with finding Two vectors u and v of R' which are linearly independent (you can see this by…

A: In the given question we have to find the the Linearly independent vectors in ℝ3. Concept: In a set…

Q: We try to fit a circle with center (C1, c2) and radius r in a least-squares sense to n given points…

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Q: #2. Find invertible matrxes B and C SO C M.B =

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Q: 14 Verify the given linear approximation at a = 0. Then deter-

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Q: 1. Explain why the following form linearly dependent sets of vec- tors. (Solve this problem by…

A: According to our guidelines we can do only one question if multiple question are posted. Please post…

Q: (d) Suppose y is a least squares solution to Cx = d (for some matrix C and vector d). Show that d-Cy…

A: Introduction: Least square approximation is a method to approximate a system of equations, mostly…

Q: Suppose vi, V2, V3, b, d are vectors in R". Further suppose that -vi + v2 + vz = -b, 2v1- 2v2 + v3 =…

A: Given v1,v2,v3,b,d are vectors in Rn.-v1+v2+v3=-b ,…

Q: 9: In the steepest descent method the vectors (Xk+1-X) and (Xk+2-Xk+1) are orthogonal for each k. If…

A: As per bartleby guidelines we only give first question answers.

Q: The set of solution vectors is linearly independent on I if and only if the Wronskian equals zero…

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Q: 21. Apply the conjugate-gradient method to the problem Ax = b, where 1 A = 1 1 %3D and b = 1 Verify…

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Q: 22) A- Find the distance between the line (y=x+3) and center of circle (x²+y²-2x=0). B- Using…

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Q: 3 4 Let y = -7 and u = -6 -4 1 Compute the distance d from y to the line through u and the origin. d…

A: The projection of a vector on a plane is its orthogonal projection on that plane. In simple words,…

Q: Consider an inner product on two P₂ vectors as (f, g) = f(-1)g(-1) + f(0)g(0) + f(2)g(2): 1) (−4 +…

A: The inner product on two P2 vectors as f,g=f-1g-1+f0g0+f2g2

Q: 8) Find the cross product a x b and verify that it is orthogonal to both a and b. a = (1, 1, -1),…

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Q: 4 Suppose v1, V2, V3 are vectors in R*, and the matrix A = v, v2 V3 has rank 1 W = Span{v1, V2, V3}…

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Q: linear algebra

A: To prove the linear independence of the three given vectors.

Q: 7) Find the Jacobian matrix at The print (1,2,1) of The Willowing Funchun: soudainish and Nidevorsh…

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Q: 18) (Section 9.7) Find the cross product in space u = 3i – 2 j+4k v=i-3j-k

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Q: 4 Let y = U2 = -7 U1 = -4 4 -6 -2 -9 Compute the distance d from y to the plane in IR° spanned by u̟…

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Q: 2- Find x, y, z, u, t, v such that 2 3 8. 3 5 +2 9 8 14 a) X =-6, y = -1,Z = -1, u = 1,t=2,v= 2 %3D…

A: xyzutv+2123456=8359814   To find : the value of x, y, z, u, t

Q: Let x = (2,1+i, i) and y = (2−i, 2,1+2i) be vectors in C3. Compute <x, y>,||x||, ||y||, and…

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Q: 2 Given u -1 and U , for which w is the set {u, v, w} linearly independent?

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Q: Verify that the vector X, is a particular solution of the given nonhomogeneous linear system. X' =…

A: Here,

Q: Solve for r and y the following system of simultaneous equations 2 In(z) = In(y) + In(16) %3D e e =…

A: Solution: As per given data e have two simple equation, 2ln(x)=ln(y)+ln(16) exey=e4 where,'x' and…

Q: the norms of a vector X = [1,12, ...,I" and matrix A = (a5) are respectively defined as ||X|| = E…

A: Given, the norms of a vector                     X=x1, x2, . . ., xnTand matrix…

Q: а? а.b а. с a? ab cos y ac cos B = b. a b? b.c = ab cos y bc cos a С.а с.b с? ас cos B bc cosa =…

A: Consider the given matrix :A=a2a.ba.cb.ab2b.cc.ac.bc2   =a2ab cosγac cosβabcosγb2bc cosαac cosβbc…

Q: 12. Given the sct of vectors S = {(6,2,1), (4,-3, 1), (5, 8, 2)} of R, is this set linearly…

A: Given: S=6, 2, 1, 4, -3, 1, 5, 8, 2 To check: Whether the set S is linearly independent and the…

Q: Suppose vi, v2, ..., m is linearly independent in V and w ɛ V. Show that v1, vz, ..., Um, W is…

A: v1, v2,......., vm is linearly independent in V and w∈V

Q: 1 5 -6 Let y = -1 , U1 = 7 4 -2 Compute the distance d from y to the plane in R' spanned by uj and…

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Q: 10.Use Cramer's rule to solve the linear system. 3x+ 5y = 8 y+z = 3

A: NOTE: Refresh your page if you can't see any equations. . system Ax=b is  the matrix A is

Q: Find the orthogonal projection of v on the solution space of the linear system Ax = 0, where v = (5,…

A: The solution is given as

Q: Consider the linear DE system æ' = Aæ with -14 -90 and A = 2 14 If the initial conditions are given…

A: To find the solution for the below linear differential equation system. x'=−14−90214x,  x0=02

Q: What are the Euler equations associated with the Lagrangian L(x, Y, Y' , z, z') = (y')²z – 3xz'y O…

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Q: (1) We have the following 4 vectors v1, v2, v3 and v4. Prove that the vectors are linearly…

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Q: 19: Find two linear operator T, and T,on V(R) such that T,T, = 0 but T,7, - 0.

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Q: (1) Suppose that {r, y, z} is a linearly independent subset of vectors in R". Show that {x - z + y,…

A: Result:  A set of vectors v1, v2, …, vn is said to be linearly independent, if a1v1+a2v2+…+anvn=0…

Q: Let v = and v3 1 for which values of S, v,, V2 , and v3 are linearly %3D V2= %3D indonondont

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Q: (1, 2, 1) on to the line x = 2+ t, y = 3 – t, z = t. Also Find Find the Projection of b = Projection…

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Q: (S.15). Let u1 =(-1,1,3), u2 = (2,1, –3), uz Find expansion of the vector v = (-3, 2, 4) via vectors…

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Q: 7. Show that the family of all solutions of the nonlinear ordinary differen- tial equation y" =y° is…

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Q: A. If the grades of the students in linear algebra and vector analysis is set to be x and y…

A: Let us denote X as the grade of linear algebra and Y as the grade of Vector Analysis. A. Excel…