One of the following vectors lies in span{ 2+x + æ2, 3+-2a2} (A) 5 + 3x + 4x2 (B) 5 + 3x + 5æ? (C) 5 + 3x + 6x? (D) 5 + 3x + 7x² (E) 5 + 3x + 8x? O (A) O (B) o (c)

Q: 2- We can write the vector x = (19,–1,–) in R³ as a linear %3D combination of the vectors x1 = (4,2,…

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Q: Find the vector in AB R2 given in the figure. 6 AB = help 4 (vectors) 1 2 3 -1 -6 -5 -4 -3 -2 -1 6.…

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

A: See the solution below.

Q: Give an example of a set of nonzero vectors in R3 that generates R3 but is not a basis for R3.…

A: Definition 1 : A basis β for a vector space V is a linearly independent subset of V that generates…

Q: Suppose and are non-zero, parallel vectors. Which of the following could not possibly be true?

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Q: Find the vector projection of b = 6î + 3ĵ + 2k onto å = î – 2ĵ – 2k.

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Q: What is the staring point of the vector i = -3i + 2j, if the ending point is (-2, 1)?

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Q: 3. Give two nonparallel vectors that are both orthogonal to (0, 5, 0).

A: Given A = (0,5,0) Let other two vectors be of type B = (a,b,c) A.B = a.0+b.5+c.0 A.B = 5b For…

Q: If vectorAB =-7i + 3j + 8k and A is the point (-2, -3, 6), find B.

A: Given : AB =-7i + 3j + 8k and A=(-2, -3, 6)

Q: - Show that the vectors X, - () 5e3t and X2 = ) 2et 7et form a linearly independent set.

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Q: Find the magnitude of the projection of (8, – 2) onto the vector (4, 7)

A: Wr have to find the magnitude of the projection.

Q: Suppose that u, ū, and w are vectors in R3 such that ūxi = (2,7, 3) and ūxu = (-5, 4,0). Find: 1.…

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Q: 2) How many different vectors are drawn here? -/

A: 3 vectors are same which has same direction and magnitude and other 2 vectors are same in direction…

Q: 6. A student claims to have found a vector A such that (2i - 3j + 4k) x A = (4i + 3j - k). Do you…

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Q: 4. Given the vectors 3 -3 -6 X1 = -2 X2 = X3 = 4 4 what is the dimension of Span(x1, X2, X3)?

A: The given vectors are,x1=3-24, x2=-32-4 and v3=-64-8

Q: 1. For non-zero vectors, a and b, show that axb =a5-(ā • 5} . %3D

A: For non-zero vectors a→ and b→ we have to show that: a→×b→2=a→2b→2-a→·b→2 Assuming, a→=ib→=j Putting…

Q: 2. Sketch the vector v = 4i – 6j. 1아 6 4 2- 10 -8 -6 -4-2 2. 4. 6 8 10 -2 -4 -8 C0 10

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Q: Two vectors ñ and m are said to be orthogonal if ñxm3D0

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Find all orthogonal vectors to u=(2, -3).

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Q: If the vectors a and b are such that a = kb where k is a positive scalar, then the vectors a and b…

A: Given statement: If the vectors a and b are such that a=kb where k is apositive scalar, then the…

Q: Find three different vectors that are in the span of the given vectors. u2 = U3 = -2 6. 2

A: The vectors which belong to the span of given vectors can be written as the linear combination of…

Q: 4. Give an example of vectors in R3 that spans R3. (show works)

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Q: 50 Express the vector b = – 11 as a linear combination of the %3D – 48 - - 14 5 - 10 - | - vectors…

A: the question are based on the concept of linear combinations. we will form the system of linear…

Q: 4 3 2 1 b. -1 -2 -3 -4 -5 -4 -3 -2 -10 1 2 3 4 5

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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: Suppose a and b are vectors such that axb=(1,

A: Given, a→ and b→ are vectors such that a→× b→=(1, 0, 2).

Q: 4 2. Decide whether the vectors (1, 2,0,-1], [2, 6, -3, -3], [3, 10, -6,-5] are linearly…

A: Given vectors are ,  [ 1,2,0,-1 ] ,  [ 2,6,-3,-3 ] ,  [ 3 ,10 ,-6 ,-5 ]  (.)  The given vectors are…

Q: 3. Explain why as n goes to infinity. the entries of the vector A" 2 go to infinity, while the…

A: To solve question 3 I will take the help of eigenvalue and eigenvector of a matrix because question…

Q: Show that the vectors (4-3) and (5,2) form a basis CF TR

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Q: uppose ā and b are two non-zero vectors in R3 and they are not parallel to each other. Then, their…

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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: How many of the vectors (n-tuples) (1 2 2 -1 ), (-4 0 0 -4), (-1 1 -2 -2 ), (-2 0 0 -2 ), (-3 -2 -2…

A: If for given vectors the zero vector can only be obtained by their trivial linear combination then…

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: Suppose that u and v are vectors in 3-space such that |u||= 5 and u · v = 7.

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Q: Suppose there is a collection of three or more two- dimensional vectors. Provide an argument…

A: Collection of two dimensional vectors mean those vector having i and j components.

Q: find two distinct vectors on the line belonging to the intersection of the hyperplanes: Xi+ 2x2 - X3…

A: We need to find two distinct vectors on the line belonging to the intersection of the hyperplanes

Q: Show that the vectors (1,1,0), (1,0,1), and (0,1,1) generate F3.

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Q: Find the orthogonal projection of the vector b =-1 on Nul(A), where -2 -2 3 -10 A = 1 -1 2 3 1 -3 3…

A: For the solution follow the next steps.

Q: Find a vector a that has the same direction as (-8, 9,8) but has length 3.

A: The solution is given below

Q: Find a vector b such that compab = 2. If a = ⟨3,0,−1⟩

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Q: Prove that swapping the order of vectors in the cross product changes the sign of the output: ьха3 -…

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Q: Show that the vectors are orthogonal.

A: Given : 3,6 and 4,-2

Q: One of the following vectors lies in span{ 2+ x + x2, 3+x- 2x2} (A) 2+ 2x + 7x? (B) 2 + 2x + 5x? (C)…

A: The linear span of the given vectors is of the form a(2+x+x2)+b(3+x-2x2)

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.