8.) find a vector of norm 2 that is orthogonal to the three vectors, u=(2,1,0), v=(-1,- 1,0) and w=(4,0,0)

Q: (1, Find a vector orthogonal to both (3, 2, 0) and to (0, 2, -1) of the form

A: The given question is related with vector space. We have to find a vector orthogonal to both 3 , 2 ,…

Q: The vectors u=(1,-2,1), v=(3,0,-2) and w-(5,-4,0) are: O not coplanar coplanar

A: We can check whether the three vectors are co planar  or not as below

Q: 8. If {V1, V2,..., ,}is a linearly dependent set of vectors, prove that one of these vectors is a…

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Q: Find the norm of the vector U(2,-6,1)

A: See the solution below.

Q: Let x and y be linearly independent vectors in R2.If | |x | |= 2 and | |y | | = 3, what, if…

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Q: u = (2, 3,-1) v= (0, 1, -2) w = (2, 4, -3).

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Q: 7. "Let &, n, ở be real numbers and consider vectors (1,5,8²); (1,n,n²); (1,0,0²). Determine the…

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Q: Q2: For the vector x=[1,5,7,9,13,20,6,7,8] replace the first five elements of vector x with its…

A: For the vector x = [1,5,7,9,13,20,6,7,8] the maximum of all co-ordinates is, 20 & the minimum of…

Q: 6. Determine whether P = and Q = 10,3,2 > are orthogonal vectors.

A: As per our guidelines we need to solve only one question. Please, repost the remaining questions as…

Q: v, =,v, =, v, =

A: To add or subtract two vectors, add or subtract the corresponding components of each vector. For…

Q: A sum of scalar multiples of two or more vectors (such as c,u + c,v + c,w, where c, are scalars) is…

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Q: (i, 2, 3i), v = Co over C. Are these vectors linearly independent? Can they form a basis 5.…

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Q: Find a linear mapping G that maps [0, 1] x [0, 1] to the parallelogram in the xy-plane spanned by…

A: Consider the given figure with the following conditions:

Q: Determine all vectors v that are orthogonal to u.u = (2, −1, 1, 2)

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Q: Show that the vectors 2 -2 2 uj = 2 uz = 3 uz = 7 1 -5 -3 are linearly dependent. Find all r1, x2,…

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Q: 2. Consider the vectors [2, 1, 0, 0], [3, 1,0, 0], [0,0, 0, 1) in R". Find a vector v so that v, (2,…

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Q: Find two vectors of norm 1, orthogonal to all the vectors u = (2, 1, 4, 0), v = (−1, −1, −2, 2), w…

A: Given data:- u=2,1,4,0v=-1,-1,-2,2w=3,2,5,4

Q: 1. Consider the vectors (2, 1,0, 2], [3, 1, 0, 1], [1, 1,0, -1] in R'. Decide whether they…

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Q: 6) a) Express the vector (8,0,5) as linear combinations of u (1,2,3), v = (2,-1,1), and w (0,1,4)

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

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Q: 2. Let y and u = Write y as a sum of two orthogonal vectors, one in Span{u} and a vector orthogonal…

A: y and u are given to us and we need to write y as a sum of two orthogonal vectors such that one is…

Q: 2 3. Show that that the vector u = -5 is a linear combination of the vectors v1 3 2 ------ 2 U2 = -4…

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Q: Decompose the vector ¯b = ⟨1, 0, 4⟩ into its projection proja¯(¯b) and its orthogonal component…

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Q: #7. Given that the three 3-dimensional vectors v1 = (- 1,3, - 4), v2 = (3, – 8, 10), v3 = (2, – 9,7)…

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Q: Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1, -4,0), v = (-1,-1,2,2), and…

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Q: -2 Show whether or not the vector bs is a linear combination of the vectors a, = az = and az = that…

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Q: 2. Write the vector v = (1,3,2) as a linear combination of vectors u = (1,2,1), %3D (2,6,5), uz =…

A: We have to write a vector v to a linear combination of the vectors u1, u2, u3

Q: 20. Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1,-4,0), v = (-1,–1,2,2),…

A: To find two vectors of norm 1 that are orthogonal to the below vectors.…

Q: 1. Consider the vectors [2, 1,0, 2), [3, 1, 0, 1), [1, 1,0, -1) in R. Decide whether they…

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Q: 19. Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1, –4,0), v = (-1,–1,2,2),…

A: Step:- 1 Given that u=2, 1, -4, 0,  v=-1, -1, 2, 2,  w=3, 2, 5, 4 Now, first we check the given…

Q: 3. 2 Find a non-zero vector in R* which is orthogonal to 1 and 2 1

A: Given vectors are 1234, 3121 and 2311. We have to find the non-zero vector in R4 which is orthogonal…

Q: What is the value of each of the constants that are part of the linear combination between the…

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Q: Find a nonzero vector orthogonal to the plane through P(2,5, 1), Q(-3, 1, –2) and R(5, –3, –1).

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Q: 8. Show that the cross product u x v of the vectors u = (-3, 5, -4) and v = (-3, -5, -5) is…

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Q: 2. Consider the vectors [2, 1,0, 0], [3, 1, 0, 0], [0, 0,0, 1)] in R'. Find a vector v so that v,…

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Q: b) Express the vector (–1,5, –6) in R³as a linear combination of (2,0, 7), (2,4, 5) and(2, –12,13).

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Q: 3. Show that that the vector u = -5 is a linear combination of the vectors vị = 3 U2 = and v3 %3D

A: Given vectors are u=   2-5  3, v1=  1-3  2, v2=  2-4-1 and v3=  1-5  7   To show that u is a linear…

Q: 2- We can write the vector x = (19,–1, -) in R³ as a linear combination of the vectors x1 =…

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Q: 1] Suppose that W, N are non-zero two- dimensional vectors which are not parallel. Show that if C is…

A: We have to solve given problem:

Q: Find all vectors in R2 that are orthogonal to u = (2,1).

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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: Find a nonzero vector orthogonal to the plane through P(2, 5, 1), Q(-3, 1, – 2) and R(5, –3, –1).

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Q: 7. Find the cross product of the vectors (a) u=(1,2,-3) v=(-4,1,2) (b) u = (0,1,- 2) v = (3,0, - 4)

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Q: 3. Show that that the vector u = |-5 is a linear combination of the vectors vị = |-3 3 2 V2 = -4 and…

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Q: determine projection of the vector b = -1 1 1 on the space generated by the vectors {--E)--[ -[+]}…

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Q: 2.2.12. Prove that two nonzero vectors x, y are orthogonal if and only if |x+y[? = [æ|2 + ly/².

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Q: Q.5. Show that the vectors V1 = ( 1, 1, 2, 4 ), V2 = ( 2, -1, -5, 2 ), V3 = ( 1, -1, -4, 0 ) and V,…

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Q: 3. Find the vector component of u along a and the vector component of u orthogonal to a for the…

A: Given that the vector u=2, 0, 1 and the vector a=1, 2, 3. We have to find the vector component of u…

Q: A2. Express v = (1,-2,5) in R as a linear combination of the vectors u; (1, 1, 1), %3D uz = (1,2, 3)…

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Q: 5. Show that if vị and vz are linearly independent vectors in R?, then any vector w E R² can be…

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