3 Let W = span Given y = 1 decompose this vector into y in W and y, in w. 3 13-

Q: Assume that 0 < a < 1 and 0 < b < 1. Find the stable vector of P 1 - b ]

A: Let w= [x y ] is a stable vector of the given matrix.  So, the equations to solve are:

Q: Find an equation of the plane that passes through the point P(2, 5, 1) and has the vector n = (1,4,…

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Q: 1. If r = xax + yay + zaz is the position vector of point (x, y, z), r = |R| and n is an integer,…

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Q: Please solve this linear algebra question. Thank you

A: According to the given information, It is required to show that u, v, w are linearly independent…

Q: 21. With A as in Exercise 17, find a nonzero vector in Nul A and a nonzero vector in Col A.

A: Given matrix is A=6-4-32-969-6 The column space of A is the space generated by the column vectors of…

Q: Find the weighted Euclidean norm of the given vector. 2. 10 with weights w = 5 v = ||v|| = Ex: 1

A: Answer

Q: The vector E %3D —а, — 4аф + За, еxpressed in RCS and in terms of ф is E 3 (-сosф + 4sinф)ax +…

A: This question is based on unit vector conversion from Cartesian to cylindrical system.

Q: Let W = span Given ỹ decompose this vector into y, in W and y, in W+. 8.

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Q: Find the flux of the vector fielol F from the baunelries of the given region (o). 37 2. (D): solid…

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Q: 8) Find the unit tangenit vector TilE) at the poin Let ř(t)= <-5t'+3, Be -S sin (E)) 3t -3t -5cos…

A: Given curve r→t=&lt;-5t5+3,3e-3t,-5sint&gt; We need to find tangent vector T→t at t=0. Tangent…

Q: 2. Find the value of a for which the vector à = (axy – z³)î + (a – 2)x²j + (1 – a)xz²k have it's…

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Q: 4) Suppose x and y are vectors in R". Prove a) r+ >f -x->f =4(x• y) b) If x and y are orthogonal…

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Q: Assume that 0 < a <1 and 0 < b <1.Find the stable vector of 1- a a P = b 1-b w = [ ]

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Q: 3) Determine whether or not the following 3D vector fields are conservative: a) (y²-z³)i + (2xy +…

A: As per the company rules we are supposed to answer only the first question and rest can be reposted.

Q: Suppose C is a curve of length N, and ||F|| < M, where M is some positive number. Prove that F. dr <…

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Q: a. A. vector.orthogenal.tr.Uxv.and.Txw.

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Q: determine if the vector v is a linear combi­nation of th e remaining vectors.

A: To determine: Find if v is linear combination of remaining vectors

Q: 1 4 17. Let a = 4 az and b = For what h value(s) of h is b in the plane spanned by aj and a2?

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Q: Consider the following. (a) Show that the set of vectors in R" is orthogonal. (v5, V5. V5) · (0, Vz.…

A: A set of vectors is said to be orthogonal if dot product of any two different vectors of the set is…

Q: (5) For every u in V, there is a vector in V denoted by u such that u + (-uu) = 0 O This axiom…

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Q: A vector u for which || u || = 1 is called a(n)_______ vector.

A: u is a vector whose modulus is 1. u=1 For a vector, if the modulus or magnitude is 1 then the vector…

Q: 6) Find the work done by the force field F(r, y, z) = ri+yjtzk in moving an object along the…

A: Work done = Force * displacement

Q: 2) If A =,find grad(div A), where r is a position vector.

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Q: 1. Show that the following vectors are linearly dependent. Uz = U3= %3D -2 3.

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Q: 1. Consider the vectors a = (1, 1, 1) and y = (1, 1, 3) in Rº. Compute æ x y. 2. Show that, for æ, y…

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Q: 1 Find the vector projection of u onto v. u= 3i- 5j ++ 2k v=7i+j- 2k

A: Please refer the attached image for complete solution.

Q: 3) (From Hardcover Book, Marsden/Tromba, Vector Calculus, 6th ed., Section 1.5., # 7 or from your…

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Q: 1-8. Prove that, for any differentiable vector u Eu(t), dv du

A: Given: ν.δνδτ=νδνδτ

Q: 025 of Axco Descube el salutons l salutions Vectare form where A is Yow eluivelent falom to the…

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Q: 5. Show that a translation t by a vector (a, b) defined by t(x, y) = (x + a, y + b) is an isometry.

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Q: Construct the vector 1.5 s+1.6t having initial point P.

A: Consider the vector ,1.5 S + 1.6 t

Q: Let x and y are orthonormal vectors in R". Then ||x - yl| is a) o b) c) d)

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Q: 1. Determine if the vectors e2t and e-t are linearly inde- e2t e-t pendent/dependent.

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Q: Find the weighted Euclidean norm of the given vector. 10 with weights w = v = ||v|| = Ex: 1

A: Here, we need to find the weighted Euclidean norm of the vector v=102 with the weights w=111. Let…

Q: Compute the integral of ſA° · dľ°P2P1 from point P1 (2,1, -1) to P2 (8,2, -1) of the vector function…

A: We have to find the integral from point p1 TP p2.

Q: Let x = (2,1+i, i) and y = (2−i, 2,1+2i) be vectors in C3. Compute &lt;x, y&gt;,||x||, ||y||, and…

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Q: 6. Let x#0 and y‡0. (a) If x 1 y, show that {x, y} is a linearly independ- ent set. (b) Extend the…

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Q: Find a nonzero vector u with initial point P(-1, 3, -5) such that u has the same direction as v =…

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Q: If u = (3, −1, 4) and v = (−2, 3, 5), the scalar projection of y onto v is:

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Q: 2. Show that the ry plane W = (r, y, 0) in R³ is generated by: (i)u = |2 and v= (ii)u = and v=

A: Please see the below picture for detailed solution.

Q: are vectors in R³ are linearly independent but ü,v,w are linear dependent. Show that there exist…

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Q: Given any vector sp S is any nonempty E. then the small 11

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Q: 1. Draw a circle with centre (1, 3). 2. Draw the three dimensional vector field for the vector xỉ +…

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Q: Let P = (-2,0, 5), Q = (3, 1, 1), and R = (0,0, 4) and define a = PQ and b= PR. Find %3D (c) The…

A: To obtain the vectors a=PQ→ and b=PR→, find the differences of the points P, Q and P, R,…

Q: Assume that 0 < a < 1 and 0 < b < 1. Find the stable vector of 1 - a а P = 1 - b [ W =

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Q: 6. Check whether Or not F= (Osxi+CysınztSinz)i is a Coservative vector - fieid

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Q: If x = (x1, x2)T , y = (y1, y2)T, and z = (z1, z2)T arearbitrary vectors in R2, prove that xTy = yTx

A: x = (x1, x2)T , y = (y1, y2)T are arbitrary vectors in R2 .

Q: 12. Suppose that ú = (a, b) is a non-zero vector in R², where a ± 0. Show that the line L =…

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Q: Let x = (1, 1, 1, 1)T and y = (8, 2, 2, 0)T . Find the vector projection p of x onto y

A: the vector projection in the direction of another vector is the orthogonal projection of a vector…