Determine whether the vectors v1=[12 1]^T , v2=[1 O 2]^T and v3=[5 6 7]^T are orthogonal vectors Non of all the above

Q: 9

A: We need to determine all the values of the constant a for which the vectors

Q: Find a non-zero vector 7 perpendicular to the vector u 12 [3]. -6

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Q: Find the vector with the given length || v || = 3, and in the direction of u = (0,2,1, -1)

A: Sol

Q: Find a non-zero vector a perpendicular to the vectors [3] and ū = 2 1

A: Given, v→ = 372  and  u→ = 121   We have to find the non zero x→ vector perpendicular to both the…

Q: 2. Choose the linearly dependent vectors in R

A: two non zero vectors V1, V2 are said to be linearly independent if and only if aV1+bV2= 0 ⇒ a=0 and…

Q: a) for which values on are the vectors V3 = 2 %3D 7 19 linearly independent?

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Q: Find a unit vector in the direction of v = ⟨−2, 5⟩ and verify that it has length 1.

A: A unit vector in the direction of v = ⟨−2, 5⟩ is given by v/|v|

Q: 4. Find the value of t such that the vectors ~v = h2t + 1,-3,3t - 2i and w = h7,4t +2,2i are…

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Q: A. Calculate the first two vectors generated by the Jacobi method. -4 1 (-6) 1 3 -1 x ={-6 x(0) =…

A: To find- Calculate the first two vectors generated by the Jacobi method. -41013-10-15x = -6-67, x0 =…

Q: Find the orthonormal set of vectors for the following set of vectors: W1 W2 =

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Q: Determine whether the vectors v1=[12 1]^T , v2=[10 2]^T and v3=[5 6 7]^T are * Linear independent…

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Q: For what values of the scalar t are the three row vectors (t,3,0), (3,t,3) and (0,3,t) linearly…

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Q: Consider the vectors x1 = (8, 6)T and x2 = (4, −1)T in R2. Determine the length of each vector.

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Q: Find a non-zero vector v perpendicular to the vector u = [ -1 ]                          [ 8 ]

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Q: Find projwv. Then decompose v into two vectors, v1 and v2, where v1 is parallel to w and v2 is…

A: If v and w are two non zero vectors, the vector projection of v onto w is  projwv=v.ww2w Substitute…

Q: 5. (a) Find two vectors of norm 1 that are orthogonal to the vectors u = (5) and pue (4 E)=

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Q: 2 1 3. Show that that the vector u = |-5| is a linear combination of the vectors v1 = |-3 3 2 2 V2 :…

A: The given vectors are: u=2-53, v1=1-32, v2=2-4-1  and  v3=1-57 Vector u=2-53 is a linear combination…

Q: Find the x-component of the vector of length 3 in the direction of V = (-1,-1).

A: v=<-1,-1>=-i-j Unit vector in the direction of vector V i.e.,     v⏜=-i-j(-1)2+(-1)2 =-i-j2…

Q: Q2) A- Use two methods to create the vector x having 100 regularly spaced values starting at 5 and…

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Q: Find a non-zero vector x perpendicular to the vectors 3 13 and u =| 4 -4 3

A: Let's find.

Q: Find bases for the spans of th e vectors in the given exercises from among the vectors themselves.[2…

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Q: Г 13 and vz = 14 are linearly independent. Determine whether the vectors v 14

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Q: to = [0 3 4 2]" v = [1 1 2 1]"

A: Handwriting solution.  { v0, v1, e1, e4} forms a basis for R4.

Q: Find all values of the scalar k for which th e two vectors are orthogonal.

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Q: For any two vectors ū and i, ||ū + u|| = ||ū|| +||7||-

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Q: Find the value for x such that the following vectors are orthogonal. 3 1 4 -2

A: The dot product of two vectors x, y in Rn is…

Q: Find a non-zero vector x perpendicular to the vectors  v= [-3]    And u = [-1]      [11]…

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Q: 17 (c) Find a unit vector which is orthogonal to the vectors -1 2 and 1 -3 5

A: First we will find a vector which is orthogonal to both given vectors and then we will find the unit…

Q: Find Projwv and Decompose v into two vectors v1 and v2​, where v1 is parallel to w and v2 is…

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Q: c) Show that vector ū = 1 cannot be expressed as a linear combination of 2 in R3 3 vectors vi 1 and…

A: we have to show that , we can not write as a linear combination of vectors v1 and v2

Q: Find projwv. Then decompose v into two vectors, v1 and v2, where v1 is parallel to w and v2 is…

A: we have to find projwv. Then decompose v into two vectors, v1 and v2, where v1 is parallel to w and…

Q: Find the coordinate vector of p = 2 – 4x relative to the basis B = {q,,q,} for P1 where q1 = 3 + 8x,…

A: Given : We are given a vector,  p = 2-4x  and a basis  B = q1, q2,                 where,  q1= 3+8x…

Q: Q2. (d) Show that u=(-2,3,1,4) v=(1,2,0,-1) and are orthogonal vectors in R4.

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Q: The orthogonal projection of the vector v =3i-j+k on the vector b 2i-j+k is

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Q: Determine whether the vectors v1-[12 1]^T, v2=[10 2]^T and v3=[5 6 7]^T are * orthogonal vectors…

A: We have to check realtion between the vectors.

Q: 3. Find two unit vectors that are orthogonal to both j +2k and į -2j + 3k.

A: Solution is here

Q: Resolve the following vectors into components: (a) The vector v in 2-space of length 7 pointing up…

A: Topic:- vector representation

Q: Q2 Given the vectors r=3i+4j-5k and s=-2J-K, where the xyz coordinate frame is obtained by rotating…

A: The given vectors are:r=3i+4j-5ks=-2j-k We have to find the cross product r×s

Q: Show that the vectors v1, V2, and v3 are linearly dependent, where n- . -. 3 V2 = 5 and v3 = 6 Vi =…

A: The given vectors are v1=12, v2=34 and v3=56

Q: Find a non-zero vector 7 perpendicular to the vector u = 5= [8]. 6

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Q: Determine a scalar x so that the given vectors are orthogonal. A = xi +-j +xk 2. B =-3i +4j + xk

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Q: When is the vector x = (3) orthogonal to the vector y = ()? You may want to go through the proof of…

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Q: Let a = 2i and b = -2i + 3j be two-dimensional vectors. Compute la – b|.

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Q: 4. Determine whether the vectors a = 2i – 3j+ 5k, b = 3i+j – 2k and c =i- 7j +12k linearly dependent…

A: To check whether the vectors are linearly dependent or linearly independent.

Q: 2 3. (a) Find two vectors of norm 1 that are orthogonal to the vectors u = -3 and v = .3 4

A: What is the inner product of the vector space of 2 by 2 matrices. We assume it is Frobbenius inner…

Q: Let u= 2 and v= 2. Show that among all the scalar multiples cv of the vector v, the projection of u…

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Q: Find the best approximation to z by vectors of the form cv1 + ¢2V2. 3 1 -7 -1 1 V1 V2 -3 3

A: To find  The best approximation to z by vectors of the form c1v1+c2v2.

Q: Find the values of ( x ) such that the vectors and are orthogonal.

A: Given: The two vectors are: 3,2,x and 2x,4,x Also, the two vectors are orthogonal.

Q: saly dla Determine whether the vectors v1=[12 1]^T, v2=[10 2]^T and v3=[5 6 7]^T are Linear…

A: Given vectors: v1=[1 2 1]T=121 v2=[1 0 2]T=102 v3=[5 6 7]T=567

Q: When decomposing the vector into the sum of two vectors, the first is parallel to the vector A = 2i…

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