--8-9--8-- 7 1. Are the vectors u =| and w= 10 independent? 4 12 2 and 3 3 independent? 5 2. Are the vectors 4 3. What is the maximum number of independent vectors we can have in R" ?

Q: In 3-D, let L be a line that does not pass through the origin. let v1, v2, and v3 be three vector…

A: We have to decide there vectors v1, v2, v3 are linearly indipendent in R3 or not.

Q: True or false: Given two nonzero vectors v and w, v can be decomposed into two vectors, one parallel…

A: Given: Two nonzero vectors v and w, v can be decomposed into two vectors, one parallel to w and the…

Q: Prove the property if a and b are vectors and m is a real number.0 . a = 0

A: Given: If a and b are vectors and m is a real number. To prove: 0·a = 0

Q: The cross product of two vectors u=(2, -3, 1) and v=(0, − 1, 2) is 5. O True O False

A: Here is the solution:

Q: . For what values of c are the vectors [−8, c, 4] and [c, c^2, c] orthogonal?

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Q: a) If possible, express w as a linear combination of vectors u and v. w = - (1,0, —7), и %3D…

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Q: Which of the following vectors is not parallel to v = (4, -2, 1). Choose all that apply. %3D O (8,…

A: We know that a vector a is parallel to vector b if a can be expressed as scalar multiple of b. Given…

Q: Determine if i = (1,0.-4) and w=(9,3,1) are parallel vectors.

A: Use the vector product to show the given vectors are parallel.

Q: Consider vectors, 2 u = |2, v = w = |-3 (a) Do these vectors line in a plane ? Why? Why not? Find…

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Q: 4. Find the vector equations for the line of intersection of the following planes: 2x – y – 5z = -14…

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Q: A vector u is a positive multiple of . Vector v = with a , what will be the signs of d, e, and f?…

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Q: Of the vectors u = (2, -1); v = (-1, -2); w = (-4, 2) and o = (4, 2) are orthogonal:   w and o u…

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Q: Determine if the vector 2 b -A = 3 5 can be written as a linear combination of the vectors ---- 1…

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Q: If vectors u =(3, 3), v=( 13. -7), and 2w +3u-v=(4,-4) what is the coordinate of vector w?

A: Since you have asked multiple question, we will solve the first question for you.  If you want any…

Q: 2) Show that if u and v are orthogonal unit vectors in R*, then. a) -4=7 b) The vectors a+v and…

A: The set of vectors u1,u2,…,uk of ℝn is said to be orthogonal unit vectors of ℝn if the inner product…

Q: b. Determine which of list of vectors The following Dinearly independent. Juihfy your. are awnser-…

A: From given vectors it is clear that

Q: Find a vector that is perpendicular to the given vectors. 3) i = (-5, 6, 7) v = 1, -9, 0) 4) RS and…

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Q: Find two vectors ?⎯⎯⎯1v¯1 and ?⎯⎯⎯2v¯2 whose sum is ⟨2,−5,3⟩⟨2,−5,3⟩, where ?⎯⎯⎯1v¯1 is parallel to…

A: We have to find v1 and V2 vector.

Q: Q1: If , r₂ and r₂ are three parallel vectors of the same magnitude Prove that ₁+₂+3 is equally…

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Q: True or false: Given two nonzero vectors v and w, v can be decomposed into two vectors, one parallel…

A: Given that : The statement : Given two nonzero vectors v and w, v can be decomposed into two…

Q: 11. Given đ = (2, x, –3) and b = (5,–10,y), for what values of x and y are the vectors collinear?

A: We have to find the values of x and y for which bothe the vectors are colinear

Q: Determine n so that the vectors m = (-2, 1, k + 1) and n = (0, 2, -3) are parallel but in the…

A: It is assumed that the question asks to find the value of k for which the vectors will be parallel…

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: (a) Consider two vectors u = 3 and v = 5 in R4, Show that 5 7 7 i) u.v = v.u ii) d(u, v) > 0 [-31

A: Two vectors u and v is given in R4, and the vector is given as:

Q: a. Without doing any calculation, explain why one might conjecture that two vectors of the form (a,…

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Q: Suppose u¯¯¯=⟨0,1⟩u¯=⟨0,1⟩ and v¯¯¯=⟨2,1⟩v¯=⟨2,1⟩ are two vectors that form the sides of a…

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Q: 9. Let ū = (4, -6), T = (-2,4), and = (6,4). (a) Are ī and ū orthogonal vectors? How about ĩ and w?…

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Q: Determine whether or not the given two vectors are parallel.u =〈4, 2, -6〉, v =〈2, -1, 3〉

A: To determine whether or not the given two vectors are parallel.u=4,2,-6 and v=2,-1,3 By definition,…

Q: Find two different combinations of the three vectors u = (1, 3) and v = (2, 7) and w = (1, 5) that…

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Q: -4 If possible, express w as a linear combination of the vectors v1, v2 and v3. Otherwise, enter…

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Q: 9. (a) are perpendicular to each other. Determine the algebraic condition such that the vectors č=…

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Q: Determine if the vector 2 b = 3 5 can be written as a linear combination of the vectors V₁ = 1 and…

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Q: Under what condition for the real numbers a,b the vectors (b,-1)(2,a) are linearly related

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Q: write the given vector in terms of I and J. u={-8, 10} u=???

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Q: 2. If A = 2a, + 0.3a, – 1.5a, and B = 10a, + 1.5a, - 7.5a,, Show that A and B are dependent vectors.

A: The solution is given as

Q: What can be concluded about non-zero vectors ū, v and w if a) ū ·v = 0 b) ūxi = 0 c) (ū x v) · w= 0

A: As per the company guidelines we are supposed to answer only first 3 subparts of the question. If…

Q: Hey, please reaply as soon as posible Consider the vectors v and w such that v = (8,0, -8) and w =…

A: Topic = Vectors correct option = b

Q: 5b- За Let W be the set of all vectors of the form Find vectors i and v in R such that W = span {i,…

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Q: (a) Suppose that a and b are two unit vectors in R^3, and a·b=11/24. Find the norm of the vector 4a+…

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Q: 3 as a linear combination of the vectors: 0 Lo] 1. Write the vector v = 6

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Q: 8. a. Using the vectors x = (3, 3, 1) and y = (-−1, 2, -3), verify that the following formula is…

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Q: 5. a. Explain why the vectors ả = (-2, 3) and b (3, –1) span R². %3| b. Determine the values of p…

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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: For the vectors ü = 2î + 3j – 2k ö = -Sî - 2j – 7k w = 3î + j – 9k the value of [(- ü) x (u – w)].…

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Q: Find two vectors a and b such that projba = <4, -2, 8>. That's all the information I was…

A: It is given that,

Q: Let a and b be vectors on R³. Suppose a = (-2, 3, 482+ 1) and b = ( 8 + 1, -2, 4) What must be the…

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Q: What is the dependence on the following vectors: u=(3.0.1), v=(1,-1,0) and w=(1.0.1) thanks!

A: A set of vectors {v1,v2,...,vn} in Rn is said to be linearlyindependent if the vector equationx1v1 +…