Question2 Let L: R R be defined by: L Find all possible 一-0 vectors u such that L U2 33

Q: 4. Let u = and w = . Find the resultant vector 4u + 5w.

A: We will find the resultant vector.

Q: Prove the Py the goreen th : ortho gonel vectors product spoce V. Prove Suppose O and v in an inner…

A: we know that ||u+v||2=<u+v,u+v> now,…

Q: 8. Suppose vị is a vector of all entries 1 in R" space, which we call "1-vector". What is ||V1||2…

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Q: The vector v with initial point (0, 0) is shown below. Write v in the form v=ai+bj, where a and b…

A: Given ,  The vector v with initial point (0, 0) We have to write v in the form v = a i + b j where…

Q: 27 Let L be the line in R³ that consists of all scalar multiples of the vector 2 Find the reflection…

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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: Let t be a fixed real number and let c = cos t, s = sin t, x = (c, cs, cs2, . . . , csn−1, sn)T Show…

A: If x is a unit vector then:

Q: -Let 1+t and tet? be vectors in P. write the vector plt) = S+ St+2t² as the lineor combination of P,…

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Q: Any vector in R perpendicular to -3 can be written in the form t, for some s, t eR

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Q: Г 26 Let W be the set of all vectors of the form Find vectors i and v in R such that W = span {u,…

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Q: Let W be the set of all vectors of the form E 11 [3a +56 [T -a Find vectors and in R³ such that W =…

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Q: Q2 (a) Let n E N and let ở, w e R". Show that if ở · w = 0, then || ở + w||2 = || ||² + ||w||². (b)…

A: This question can be solved using the concept of dot product of two vectors.

Q: Question 2. Using the inner product (p, q) = L p(x)q(x)dx on P2, write v as the sum of a vector in U…

A: given inner product p,q=∫01pxqxdx v=x2 , U=spanx+1,9x-5 claim- write v as sum of a vector in U and a…

Q: c. Suppose there is a vector w with u w =

A: Note: As per our guideline we can not author a handwritten solution. Introduction: The dot product…

Q: Let S be the parallelogram determined by the vectors 6. -3] Let A The area of the image of S under…

A: The given vectors are : b1→=-23 and b2→=-25. The given mapping is: x→↦Ax→, where A=6-3-32.

Q: Defined by T(x) = Ax, find a vector x whose image under T is b, and determine whether x is unique.…

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Q: A vector A-xyzi+3x'yj+ (xz-y'z) k.

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Q: 16. Let F = 2a, - 6a, = 10a- and G = a, + G,a, + 5a;. If F and G have the same unit vector, G, is…

A: In geometry and physics and its engineering applications, we use two kinds of quantities, scalars,…

Q: -3 3 Let u = -5 and i: 7 Find a vector w not in span {u, v}. 4 -3

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Q: Let a be the anqle between the vectors u=(3,0,4) and v=(4,0,3). Then * O cos(d) = 24/25 O None of…

A: Introduction: The dot product of two vectors always produces a scalar quantity. When two vectors…

Q: _3. Let x be a convex combination of {y1, . . , yk }. Assume in turn that each y; is a convex…

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Q: -3 6. Let u = 0 |and i =| 1 Find a vector ü not in span {u, v}. 1

A: A vector w→ does not lie in the span of the vectors u→,v→ if determinant of the matrix formed by…

Q: Let v=2i-5j and w =3i+7j Find the specified vector v+w 3v

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Q: Which of the following vectors is in set S = Span { vi = , V2 = V3 = 3 3

A: See the attachment

Q: [3] that are 25. Let v = Describe the set H of vectors b. orthogonal to v. [Hint: Consider v = 0 and…

A: Two vectors are orthogonal if they are perpendicular to each other. That means if the dot product of…

Q: 6) Let U be the plane spanned by the two orthogonal vectors and in R. If v = (0), which one of the…

A: I think given options are incorrect.

Q: Question 11. Let R³ have the Euclidean inner product, -1 2 and W = span{u1, U2}. Uj = U2 = v = %3D…

A: As you have asked three different questions(in terms of logic and answer of one are not required for…

Q: let V be the Euclidean space R3 with the standard inner product.

A: Given:          u = 11-2  and  v = a-12 To find :             The values of a, for which u and v…

Q: Question 3. Let v and w be vectors in inner product space V. Prove that v is orthogonal to w if and…

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Q: Question 3. Let v and w be vectors in inner product space V. Prove that v is orthogonal to w if and…

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Q: o find the image of v and the preimage of w. , 2vq – v2 ), v = (1, 1), w = (-7/7, 2, -20) age of v…

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Q: -4s – t Let W be the set of all vectors of the form 5s + 3t |. Find vectors u and v in R such that W…

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Q: iven belo

A: The value of derivative of vector R→t, R'→t=2e2t-4,6t2,1t-1  Integrating the derivative vector with…

Q: 4. Let u o, where o is the zero vector. Show that there are exactly two unit vectors that is…

A: This is a problem of vector algebra.

Q: За + 2b Let W be the set of all vectors of the form Find vectors u and i in R' such that W = span…

A: We need to find the vectors u→ and v→ such that W=span{u→, v→}

Q: [6 Let j = 1 and i = Write j as the sum of two orthogonal vectors, i in 8 Span{u} and i2 orthogonal…

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Q: (1) Let x and y be the vectors x = and y = 4 (la) Find a vector z such that ||z|| = 1 and z is…

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Q: The vector w is a unit vector, and the vector i is any non-zero vector. If z = (x · W)w and ỹ = i –…

A: Use the property of dot product and associative and distribute property to solve the problem.

Q: The vector v with initial point (0, 0) is shown below. Write v in the form v=ai+bj, where a and b…

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Q: 4) Find all vectors vE C? such that (1 + i)v + () = () 3+ 6i

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Q: Let S be the parallelogram determined by the vectors b, 8. and b2 = 2 Compute the area of the image…

A: Given that S be the parallelogram determined by the vectors   The area of the parallelogram S is…

Q: and v2 = -3 3. be two -8- Question ( Let vi %3D vectors in R. Show that v belongs to span {v1, v2 }.

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Q: a Let v= b Describe the set H of vectors y that are orthogonal to v. [Hint: Consider v= 0 and v ±0.]

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Q: Let W = {[x]∈ R2^ | y > or equal to 0} .             [y] (a) If u and v are vectors in W , is u + v…

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Q: 1. Consider the vectors x¡ = (8, 6)' and X2 = (4, –1)' in R?. %3D (a) Determine the length of each…

A: (a)

Q: V= 12 a. u= NOTE: The span of a finite number of vectors is the set of all finear combinations of t

A: We know that given vector "U" is Linear combination of V1, V2, V3   if U=xV1+ yV2+ zV3…

Q: Question 2. Using the inner product (p, q) = S p(x)q(x)dx on P2, write v as the sum of a vector in U…

A: It is given that: p,q=∫01pxqxdx and U=spanx+1,9x-5 Let px=ax2+bx+c and px,x+1=px,9x-5=0

Q: Q1. In each part determine whether the given vectors are orthogonal with respect to the Euclidean…

A: Two vectors u , v are orthogonal if and only if u.v=0 (a) Given u = 2 , 3 , -1 , 0v = (3 , 6 , -2 ,…

Q: S Let H be the set of all vectors of the form Find a vector v in R’ such that H = span { ú}. -S -2s

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