Consider linear independent vectors v=(a,b,c) & w=(x,y,z) in R. Let be a linear combination of i & w. Are Ŝ & w linear independent?

Q: Suppose v, w, z are vectors in R". Show that if r and y are linear combinatio: v, w, and z, then r+…

A: Linear combination of the vectors

Q: In Fn, let ej denote the vector whose jth coordinate is 1 and whose other coordinates are 0. Prove…

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Q: Let v, w, and a be nonzero vectors such that v · a = w · a.Is it true that v = w? Either prove this…

A: Given: v, w and a is non zero vectors, such that: v·a=w·a To prove: v=w

Q: Please solve this linear algebra question. Thank you

A: According to the given information, It is required to show that u, v, w are linearly independent…

Q: Let y= and u= 3 Write y as the sum of a vector in Span (u) and a vector orthogonal to u.

A: Describe y as the sum of vertices x1 in span u and x2 orthogonal to u         x1=α9, 3=9α, 3α and…

Q: Verify the Pythagorean Theorem for the vectors u and v.u = (1, −1), v = (1, 1)

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Q: Are the Following Vectors Linearly Dependent or Independent? 1) (3,4), (4,3) Ans. Independent

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Q: Consider linear independent vectors v=(a,b,c) & w=(x,y,z) in R. Let 5 be a linear combination of v &…

A: In the theory of vector spaces, a set of vectors is said to be linearly dependent if there is a…

Q: Let y = and u = Let L be the line spanned by u. Write y as the sum of two orthogonal vectors, YL in…

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Q: Let v = 2i - 5j and w = i - j.Decompose v into two vectors, v1 and v2, where v1 is parallel to w and…

A: v=2i-5j  and  w=i-j. Now, v·w=2i-5j·i-j=21+-5-1=2+5=7 & w=12+-12=2

Q: Find all vectors in R* that are orthogonal to both 1 1 V1 = and V2 2 -2

A: Linear Algebra: The vectors are: v1=112-2v2=2112Let denote the vector v3=v1v2v3v4

Q: Determine if the vector v is a linear combination of the remaining vectors.

A: Given vectors are: v=123; u1=110; u2=011 If the vector v is a linear combination of the remaining…

Q: Let u = (-1,0,1), v= (3,2,1) and w= (0,1,2). (b) Prove that the vectors u v and w are linearly…

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Q: Show that the vectors 1 – t,1+ 2t² , t² +t+1, t² + 2tare linearly dependent and indicate how one of…

A: Given Vectors:V1 = 1-tV2 = 1+2t2V3 = t2+t+1V4 = t2+2tgiven vectors are linearly dependent, then…

Q: Verify the Pythagorean Theorem for the vectors u and v.u = (4, 1, −5), v = (2, −3, 1)

A: Given   The vector u = (4, 1, −5), v = (2, −3, 1) Pythagorean Theorem for the vectors

Q: If a, B, y are linearly independent vectors of V(R), show that a + B, B + y, Y +a are also linearly…

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Q: show that the given vector functions are linearly independent on (−∞,∞).

A: To show that the given vector functions are linearly independent x1t=   et-et,        x2t=etet

Q: 2. Let uv,w.z be vectors in R. Show that if u and v are linearly dependent, then (u,v.w.z} is a…

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Q: Are the following vectors Linearly Independent? Show your work vų = [2 4 – 5], v2 = [7 2 – 1],v3 =…

A: Let x, y , z be three scalers. Condition for these vectors to be independent :

Q: Prove that if vector u is orthogonal to both vectors v and w, then u is orthogonal to v + w.

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Q: Determine whether the following vectors are linearly independent in R2:

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Q: (a) Show that the vectors v1 = (1, 2, 3, 4), v2 = (0, 1, 0, – 1), and v3 = (1, 3, 3, 3), form a…

A: (a) The given vectors are: v1=(1,2,3,4), v2=(0,1,0,-1), v3=(1,3,3,3)

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: Let x and y be two orthogonal vectors. Then prove that +

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Q: Find the coordinate vector of w relative to the basis S= = (u1, u2) for R. Let u = (2, –3), u2 = (3,…

A: Given

Q: Let y = 18 || = and u = 6 Write y as the sum of two orthogonal vectors, ₁ in Span {u} and ₂…

A: Given that                   y→=-4-3 and u→=66.

Q: Let v = 2i - 5j and w = i - j. Decompose v into two vectors, v1 and v2, where v1 is parallel to w…

A: Given vectors are: v = 2i - 5j and w = i - j The formula for the vector projection is given by…

Q: Let B = {v2, v2, . . . , Vk} be a set of orthonormal vectors, this is, vi vj 0 if i # j and v; · Vi…

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

A: The solution is follows:

Q: Let u = (-1,0,1), v= (3,2, 1) and w = (0,1, 2) . (a) Prove that the vectors u – v, u+ v and u x v…

A: Given : u=<-1,0,1> v=<3,2,1> w=<0,1,2>

Q: Let u, v, and w be vectors in R". If u • v and u•w are both nonzero then v and w are not orthogonal.

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Q: Find the value of h for which the vectors are linearly dependent

A: The given vectors are 1-14 , 3-57 , -15h The vector v3 are linearly dependent if the equation…

Q: Determine whether the set of vectors in P, is linearly independent or linearly dependent. S = {x?, 1…

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Q: Let x = (1,2,3) and y = (1,1,1) Project y on x (in econometrics, this may be denoted by Px). Are the…

A: We will first write the formula for projection of a vector onto another vector b .

Q: Let u, v and w be vectors in Cn . Clearly prove that (u + v) · w = u · w + v · w.

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Q: If X and Y are linearly independent vectors in R", then {0,X,Y} is linearly independent.

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Q: Exercise 6 Is the set of vectors V = {i² + 2t – 1,3t + 5, -t² + t + 6} linearly dependent?

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Q: Determine if the vector v is a linear combination of the remaining vectors.

A: The given vectors are, v=321,u1=110,u2=011

Q: Find x if the vectors a =i+j+ 2k;b = xi-j+k; coplanar or linearly dependent.

A: Given,       a=i+j+2kb=xi-j+kc=3i-2j-k

Q: Determine whether the vector U = 2 is a linear combination of the vectors Xi = 2 X2 = and X ? Give…

A: Let  U→=aX1→+bX2→+cX3→  Where, a,b and c are scalar. Then,…

Q: 3. Consider two vectors v = and w =. (a) Decide if v and w are linearly independent.

A: (a) Given v = <0, 1, 2>  and  w = <1, 0, 1> Let av + bw = 0 => a(0, 1, 2) + b(1, 0,…

Q: Consider the set of vectors {u" ,v ,w° } in R°, where u =(4,-4,8), v =(9,6,3) and w =(-9,-21,k),…

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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 = u − v + w

A: Given:                                                          u = <1, 2,…

Q: Show that if u and v are linearly independent vectors, then so are  u + v and u -v.

A: Given :           u and v are linearly independent vectors.   To prove :               u + v and…

Q: A set of vectors S={v in a vector space is called linearly independent if the vector equation c…

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Q: There are 6 linearly independent vectors in R°. O True False

A: We know that the dimension of the vector space R5 is 5.

Q: Determine if the vectors of R³; vị = (1, –3,0), v2 = (3,0,4) and vz = (11,–6,12) are linearly…

A: Given vectors are: v=(1,-3,0) v=(3,0,4) v=(11,-6,12) Form a matrix by having rows as given vectors.…

Q: Write y as the sum of two orthogonal vectors, x1 in Span{u} and x2 orthogonal to u

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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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