Given the two vectors V. = 8 and v, = Choose a vector v so that the set {v, v, v}is linearly independent in R3. 1' -36 32 28 -42 38 -33 32 27 42 -38 3 None of the others

Q: Consider the following vectors. u (6, –5) and v = (9, 1) u + v = (12, – 3) | (c) Find 7v – u. 7v – u…

A: By algebra of vectors we solve the this question.

Q: If S is a function of (x, y, z) coordinates, and P = Ai - Bj - Ck where i, j, and k are the unit…

A: S is the function of (x,y,z) and P→=A i-B j-C k i, j, k are unit vectors. Solution 1: ∇×∇·∇S Since…

Q: Let vy = (1,0, -2), v2 = (-2, 1, 7), v3 = (h. –3, –-5) be three vectors in R³. For what value(s) of…

A: Given vectors from the vector space ℝ3 are v1=1, 0, -2, v2=-2, 1, 7 and v3=h, -3, -5. We have to…

Q: Let u, V and w be three vectors in R. Which of the following is not defined for all u, v and w?…

A: Given u , v and w be three vectors in R3 . To find which of the following is not defined :-

Q: If v . w = 0, then the vectors v and w are________.

A: Lets two vector be v and w. v.w = v × w × cosθ Where theta is angle between v and w.

Q: Consider vectors v' and w' such that: v =(2,6,4) and w =(a+3,a,4a+1), with a constant real. If it is…

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Q: 15. Given three independent vectors w, "'z innd wz, let 2 2=[Wi #2 #3 2 1 0 1 c Then, the vectors v,…

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Q: Given vectors vi = |2 and v2 = 3 V1, Vị and v3 is linearly independent. find a vector v3 in R so…

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Q: For what value(s) of k are the vectors u = in R orthogonal? k v= -2

A: Here we have to find the value of k such that u=1k3 and v=k2-2-1 in ℝ3 orthogonal.

Q: For what values of h the vectors -3.72%3D linearly independent are

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Q: -Let 1+t and tet? be vectors in P. write the vector plt) = S+ St+2t² as the lineor combination of P,…

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Q: Which of the following pairs of vectors are linearly independent? u = (1,0) and w = (0,2). u = (1,2)…

A: Given: Some pairs of vectors. To find: Which of the pairs are linearly independent. Linearly…

Q: a) Find the value(s) of c for which the following vectors vị = ,v2 = --- 1 and v4 are linearly…

A: According to our guideline we are supposed answer only the first question if you want any particular…

Q: If v . w = 0, then the two vectors v and w are____

A: If v . w = 0, then the two vectors v and w are____

Q: If v=3w then the two vectors v and w are ................

A: Given :                    If v = 3w, then the two vectors  v and w are ____________

Q: Which of the following pairs of vectors are linearly independent? u= (1,2) and w = (-2,-4). u= (1,0)…

A: If an ordered pair (x,y) can be written as k(x,y) for k any integer.

Q: Which of the following pairs of vectors are linearly independent? Du = (1,2) and w = (2,1). Ou=…

A: I am attaching image so that you understand each and every step.

Q: Given vector U= ⟨1,-1⟩ and V=⟨1,1⟩, find a linear combination of the vectors u and v of the form aU…

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Q: Consider the following vectors: 2 3 u = 3 v = -4 W = 17 2 Express w as a linear combination au+bv.…

A: The given vectors are  u=23-1  , v = 3-42,  w= 017-7

Q: a) Find the value(s) of c for which the following vectors vị 1 ,V3 and v4 -1 1 are linearly…

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Q: If v*w=0, then the two vectors v and w are................ .

A: The question is taken from the vector in which we have to prove the given vector identity and given…

Q: Which of the following vectors is parallel to the vector v -2i +j+ 2k O 2i -j-2k O 4i + 2j + 4k O 2i…

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Q: a. Consider the following vectors in R3 V1 = Vi = |2|,v3 1 Is the set consisting of these vectors…

A: Let's find.

Q: 3. Let u, - 2. u, 1. Let u, = v,. Find a vector v, in the span{u,u;} that is orthogonal to and v; v-…

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Q: For what value of x, are the vectors vị 3 V2 = 3 and v3 = 2 linearly dependent? 3 Select one: 10 9.…

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Q: Suppose for vectors u, v and w that – 3u + 5v + 2w = 0. What does this say about the set {u, v, w}?…

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Q: Consider the vectors v1, V2. Assume that they are linearly independent. Take a vector v that is not…

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Q: Find the vector z, given that u = ⟨1, 2, 3⟩, v = ⟨2, 2, −1⟩, and w = ⟨4, 0, −4⟩.     z = 5u − 3v −…

A: Given: u=1,2,3, v=2,2,-1, w=4,0,-4 for finding given vector z, we use given values

Q: (iii) Suppose the vectors u, v, w are linearly independent. Show that the vectors u+ v, u-v, u-2v +w…

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Q: Given the points A(-2, 3, 1), B(0, 0, 2), and C(-1, 5, -2) Express the vector v = (3,2,7) as a sum…

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Q: If --0--0---0 1 and v3 = 0 then the vectors V1, V2, and v3 are linearly dependent. Select one: O…

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Q: Given two vectors t = (1,2, 3) and ở = (1,0, – 1), find (a) t . ở (b) a vector that is orthogonal to…

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Q: 41. For what values of t are the following pairs of vectors parallel? (a) 27 + (r² + 71 + 1)j +ik,…

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Q: Find the value(s) of c for which the following vectors v, = 1 and v4 -1 1 are linearly independent.…

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Q: If v.w 0, then the vectors v and w are

A: We know that two vectors u and v are said to be orthogonal if u . v = 0.

Q: Given the points P1 (5, 4, 3), P2(1, 5, –2) and P3(10, –2, 5). Find the vector that is orthogonal…

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Q: Suppose u, v, w are linearly independent vectors. Prove that S is linearly independent where (a) S=…

A: A set of vectors v1 , v2 , v3 ,...,vk from a vector space V  is said to be linearly independent , if…

Q: For any two vectors u, v E E such that u v and ||u|| = 12 21 a 17

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Q: Given the vectors u = (2,1,1,1) and v = (3,2, −1,2), find the value(s) of t such that I.  v . (u +…

A: Given vectors are u=2,1,1,1 and v=3,2,-1,2. To find value of t such that v.u+tv=16. Solution:…

Q: Let v and be two nonzero vectors in R' and 0 be the angle between 4. (" and . If and are linearly…

A: Given query is to find the angle between vectors when they are linearly dependent.

Q: - Let v and w be vectors such that |v| = 2, ww = 36 and the angle between v and w is T/3. Calculate…

A: This question can be solved using the concept of vectors.

Q: Given vector U= ⟨3,1⟩ and V=⟨-4,3⟩, find a linear combination of the vectors u and v of the form aU…

A: Solving simply equations and find the value of a and b by compairing both side of vector

Q: Given v = i + 2j, w = 3i + 6j, find projw v. Then decompose v into two vectors, v1 and v2, where v1…

A: v=i+2j, w=3i+6j Now, v·w=i+2j·3i+6j=13+26=15 & w=32+62=45 Therefore,…

Q: The vectors w = x= y = and z = are linearly independent. O linearly dependent. If the vectors are…

A: The solution is follows:

Q: given the vectors from R, (-5 0 3) belongs to span{v,, V2, V3}. Select one: O True O False

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Q: Consider the sets of vectors  S={u,v,w} and T={u,v,w,x}. Which of the following is true:  -If T is…

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Q: Which of the following vectors is parallel to the vector v -2i +j-2k O 4i-2j+ 4k O 2i-j-2k O 2i…

A: the vector will be parallel if they are multiples of one another that is u=cv

Q: Which of the following vectors are linearly independent? B) [1 2 3] 37 206 S75 R이 기이 46l GaF

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Q: Which of the following vectors is parallel to the vector v = 2i -j– 2k O 4i – 2j + 4k O 2i + j+ 2k…

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Q: Given the functions 2x and |x|, show that (a) these two vectors are linearly independent in C[−1,…

A: (a)  The linear combination of two given functions is  2xc1 + xc2 Now , put x=1 and -1, we get two…