Given the ordered basis -5 B uj = U2 = 13 with respect to B. -12 find [v]B, the coordinates of v = Ex: 5 v]B =

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: Find the coordinate vector of p relative to {p,» P;» P3} for P,. the basis S =

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Q: Given the vectors u = (-3, 1, 2), v = (1, 2, 1), and w = u + mv, determine the value of m so that…

A: The given vectors are u=-3,1,2,v=1,2,1 and w=u+mv. We have to find the value of m.

Q: Let A and B be nonzero vectors. Find k e R such that A – kB is orthogonal to A + B.

A: We know if a vector P→ is orthogonal to another vector Q→ then scalar product (dot product) is zero.…

Q: Given the ordered basis B - {m = ["] = {u1 , U2 find [v]g. the coordinates of v = with respect to B.…

A: Let β= u1 , u2 , ...... , un    be an ordered basis for a finite dimensional vector space V. For x ∈…

Q: Given the ordered basis B = {ui U2 = 13 with respect to B. -12 find [v]B, the coordinates of v = Ex:…

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Q: What is [v]B, the coordinates of v = with respect to the standard basis B : of R?? Ex: 5 : [v]B =

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Q: Given two vectors e1=(1, 0, 0)T and e3=(0, 0, 1)T in the 3D space, figure out c) e1 × e3

A: Given two vectors e1=(1, 0, 0)T and e3=(0, 0, 1)T to Find e1 × e3

Q: Consider the following three vectors a, b and c 10 -4|,b 5,c = 7 a = 3 Lt + 3. For which values of…

A: To find the value of t.

Q: c for which the following vectors vi = %3D 1 P4 = are linearly independent. 1

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Q: 1. Given the vectors U = i – 2j+k, V = 2i+j+k and W = 3i – j+2k, compute the following: (a) U. V (b)…

A: Given vectors   u = i^ - 2j^ + k^  ,  v = 2i^ + j^ + k^and w = 3i^ - j^ + 2k^We find a u.v b u×v c…

Q: compute the vector v if the coordinate vector vS is given with respect to each ordered basis S for V

A: Given that, S=1-200,-1301,1000,0-110Also,vS=0102

Q: Compute  the  coordinate  vector  of  v with  respect  to  given ordered  basis  S  for  V . V is P1…

A: Given: v→=t+4 Ordered basis for v→ :  S = {t + 1, t − 2}

Q: 27. Given the vectors a and b, where a = 21 – 2j + 2k and b = 3i – j + 2k are coplanar vectors, a x…

A: Given vectors are a=2i-2j+2k and b=3i-j+2k are coplanar vectors. To find: a×b Solution: We have…

Q: Find out Vector S= { V, V2, V3} is the Basis por R. if VI : ( 3,1,-4), Vz C2,s,6), V3 - C1,4,8) %3D…

A: Here we have to find whether v1 , v2 , v3 are basis of R3 or  not.

Q: Consider the following. u = -8i – 4j - 2k, v = 4j + 4k (a) Find the projection of u onto v. -3j – 3k…

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Q: Decompose V into in two vectors V1 and V2, where V1 is parallel to W and V2 is orthogonal W. V=2i+j…

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Q: Let a = 2i – j - 3k and b = 3i – j-k %3D (a) C ) Find two unit vectors orthogonal to both a – i and…

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Q: Given the vector v has an initial point at (-8, 5) and a terminal point at (-3, –1), find the exact…

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Q: Given the ordered basis B , U2 5 find (v]B, the coordinates of v : with respect to B. Ex: 5 (v]s

A: Given: and Notice that v=u1. So, it can be observed that v=u1+0u2.

Q: Given the points C(-4, –5) and D(-1, 1), express the vector CD in terms of i and j.

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Q: Given the following vectors, let W Span{v, v2, vs}. v3 (a) ( . Is z in W? Why or why not? (b) ( Find…

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Q: Find b so that the vectors v = i + jand w = i + bj are orthogonal.

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Q: Given v = - 3i + 5j and w = i+j, a. Find projwv. b. Decompose v into two vectors V1 and V2, where V1…

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Q: The set B = {1 – t2, t – t², 2 – t + t²} is a basis for P2. Find the coordinate vector of p(t) = 1+…

A: The coordinate vector of p(t) relative to B will be [p(t)]B

Q: Consider the basis B of R? consisting of vectors and Find i in R? whose coordinate vector relative…

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Q: Given v = - 7i + 5j and w= -i+j, a. Find projwv. b. Decompose v into two vectors v, and v2, where v,…

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Q: и %3D —3і + бј, w%3 -2i – 5j u = W =

A: Here I am attaching image so that you understand each and every step. Given option are not match…

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

A: Note:- We are entitled to solve only the first question, unless specified. Given vectors: a=3i-j+4k,…

Q: Find a unit vector orthogonal to A in the plane of B and C if A = 2i - j + k, B = i + 2j + k, and C…

A: The given details are as follows.

Q: Given the vectors P=3i - j +k, Q =4i +Qy j-2k, and S=2i -2j +2k,determine the value of Qy for which…

A: given the three vectors P=3i-+j+k , Q=4i+Qyj-2k  and S=2i-2j+2k are coplanar vectors. we need to…

Q: Let TiPe s Pe, T(ax?+ bx+c) = 2Qx+ b. Then the basis of NIT)

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Q: Find the coordinate vector for w relative to the basis S= {u1, u2} for R2. uj = (1, 0), u2= (0, 1);…

A: Here we use basic defnition of change of basis coordinate

Q: Find u × v and show that it is orthogonal to both u and v.u = j + 6k, v = i − 2j + k

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Q: Find the coordinate vector of w relative to the basis S = { u1, u2} for R u 1 = (4, – 4), u 2 = (4,…

A: Given: u1=4,-4u2=4,4w=0,24

Q: Given the vectors V1 = (x, 1,1), V2 = (1, x, 1) and V3 = (1,1, x). S = { V1, V2, V3} of the set Find…

A: 3 vectors form a basis of R3, if they are linearly Independent. Vectors are linearly Independent if…

Q: Given a vector Á = 3a, + 2a, + 6as , determine the vector component of Á perpendicular to the…

A: Topic:- vector

Q: Given v = 3i - 2j, w = 2i + j, find projw v. Then decompose v into two vectors, v1 and v2, where v1…

A: Given that, The vectors  v = 3i - 2j, w = 2i + j. We have to find projw v By using a formula, projw…

Q: 2. Given a force vector F= -381 + 2z + 783 (kg m/s) and the DCM ape CSW = b q n de determine the…

A: Here we solve the given problem.

Q: Find a basis for the space spanned by the given vectors, vl.,., v5. [M]

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Q: In P, consider the basis B- {6,6} where 1 %23 b2 I – 4 Task Find the coordinates of vector w = 2z +…

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Q: Given the ordered basis -8 -3 B = uj U2 = 7 , U3 1 4 7 find [v]B, the coordinates of v = 22 with…

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Q: :Consider the basis B of IR? consisting of vectors and 3 Find i in R? whose coordinate vector…

A: The given basis B for ℝ2 is: B=-75, -12 Find x→ in ℝ2 whose relative to the basis B is: x→B=3-5 Let…

Q: Given an orthogonal basis B and a vector v, find the B-coordinate vector of v. V 8. b) B =

A: Let B=v1,v2,…,vn be a basis for a vector space V and v be any vector in V. The vector v can be…

Q: (b) Find the values of s such that vectors -si – 2j+ 5sk and 9si + j+3sk are orthogonal.

A: The given vector are -si-2j+5sk and 9si+j+3sk

Q: O Are the three vectors: V= 4i-8j+kV= 2i+j-2k and ū;=3i-4j+12K in the Same Plane?

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Q: Given v = 6i + 2j and w =i-j, a. Find projwv. b. Decompose v into two vectors v, and V2, where v, is…

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Q: s such that vectors –si – 2j+5sk and 9si +j+3sk are orthogonal.

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

A: Show that the vectors a = 3i−j+4k, b = i−3j−2k and c = 4i−3j+2k are linearlyindependent. Find…