49. Show that in the vector space V, (R), the vectors (1, 2, 3), (- 2, 1, 4), (- 1, – 1/2, 0) form a dependent set.

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

A: See the solution below.

Q: Suppose V1, ..., Vn are vector spaces then does L(V1 x...x Vn, U) have the same dim with L(V1, U)…

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Q: 5. Determine the number of vectors (x1,...,x„), such that each x; is either 0 or 1 and i=1

A: (x1,x2,...,xn) is a vector with xi is either 1 or 0.  Now, ∑i=1nxi ≥ k implies at least k of the…

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: Verify the Cauchy-Schwarz Inequality for the vectors.u = (1, 1, −2), v = (1, −3, −2)

A: By Cauchy-Schwarz Inequality for the vectors, we have

Q: 8. Suppose v1 is a vector of all entries 1 in R"¹ space, which we call "1-vector". What is ||v1||2…

A: Given that, Suppose v1 is a vector of all entries 1 in ℝn space, which we call 1-vector. What is…

Q: Let W = span Given ỹ decompose this vector into y, in W and y, in W+. 8.

A:

Q: 3. Show that the vectors v, = (0, 3, 1, -1); v, = (6, 0, 5, 1); v; = (4, -7, 1, 3) form a linearly…

A:

Q: Show that a set of vectors {v,, v2. ..., V5} in Rn is linearly dependent when dim Span {v,, v2, ...,…

A: We need to show that: {v1, v2, v3, v4, v5}  in Rn are linearly dependent when  dim Span{v1, v2, v3,…

Q: (3) The subset of pairs {(r, y) E R²|ry = 0} in the vector space R².

A:

Q: What are the conditions for a set of vectors {ai , i ∈ [1, N]} to form a basis for an N dimensional…

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Q: Q6: Show that R³ = {(x1,x2, x3)|lx1,x2, x3 E R} is a vector space

A: Vector space is the field created by set of vectors with specified direction and magnitude, usually…

Q: The two vectors u=(-2,3,1,4) and v= (1,2,0, -1) are orthogonal in the vector space R4 True False

A:

Q: (9) Show that the space curve given by the vector equation r(t) = passes through the point (1, 4,0)…

A: Explained below

Q: Show that the vectors v, = (0, 3, 1, -1); v =(6, 0, 5, 1); v (4, -7, 1, 3) form a linearly dependent…

A: Given vectors v1 = (0, 3, 1, -1); v2 = (6, 0, 5, 1); v3 =(4, -7, 1, 3) . Let c1. v1 + c2. v2 + c3.…

Q: 3. Show that the vectors v₁ = (0, 3, 1, -1); v₂ (6, 0, 5, 1); v =(4, -7, 1, 3) form a linearly…

A:

Q: Let (V, (,)) be an inner product space and let f, g be vectors in V. If || F|| = 4. ||g|| = 5 and ||…

A:

Q: Suppose that u and v are vectors in 3-space such that u ||= 5 and u · v= 7. Find: (a) u · u = (b) v…

A:

Q: 5) Suppose that the set of vectors {ỉ, 7, w} is linearly independent. Prove that Span({ū, T}) #…

A: Given that u→,v→,w→ is linearly independent. Prove Spanu→,v→≠Spanu→,v→,w→.

Q: 3. Show that the vectors v = (0, 3, 1, -1); v, =(6, 0, 5, 1); v, = (4, -7, 1, 3) form a linearly…

A: Given the three vectors

Q: Let F = 3 x R, where is a constant vector. Calculate F. dR C on the line segment C connecting (1, 3,…

A: According to the given information, it is required to calculate the integral.

Q: Show that the vectors v, = (0, 3, 1, -1); vz = (6, 0, 5, 1); vz = (4. –7, 1, 3) form linearly…

A: Solve the given problem.

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

A:

Q: Verify the Cauchy-Schwarz Inequality for the vectors.u = (6, 8), v = (3, −2)

A:

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)

A:

Q: The initial and terminal points of the vector v are (x1, y1, z1) and (x, y, z). Describe the set of…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

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: . Show that the vectors V1=(0, 3, 1, -1); V2=(6, 0, 5, 1); V3=(4, -7, 1, 3) form a linearly…

A:

Q: 1 Let u1 = 3 U2 = -1 , Uz = ,X = then write x as sum of two vectors -3 3 on in span {u1} and other…

A: Given, u1=1101 u2=-13-1-2 u3 = 101-1 x=1-1-33

Q: Let ū = [1,1,0] and w = [2, 2, 1]. Find the projeci proj,u of the vector w on ū a) [1,0, 0] b) [0,…

A:

Q: Let u = (1, 3), v = (2, 1), w = (4,−1). Find the vector x that satisfies 2u −v + x = 7x + w.

A:

Q: What is the dimension of the vector space spanned by the vectors v1, v2? v1 = (6, -2, 4) and v2 =…

A: v1 = (6, -2, 4)  v2 = (14, 2,8)  There does not exist any real number c such that v1 = c v2 hence v1…

Q: (9) Find a vector parameterizat1on of the line r(t) which passes through the points P = (2, –6, 4)…

A: The given points are P=(2,-6,4) and Q=(3,5,-3). We have to do vector parametrization. We subtract…

Q: Ui=(1, 1, 1, -1) Uz=(5, 1, 1, 1) Uз-(-3, -3, 1, -3)

A:

Q: The vector norm is always positive.(i.e. ||X||>0 for every vector X.) Select one: O True False

A:

Q: 2. Suppose that u, v and w are vectors in 3-space such that ||u|| = 5, u·v = 7, and u · w = -3 а.…

A: Answer

Q: 2. Let . t, t3, , be vectors such that t E span{t, , ta} then span(r, 2, a, a) = span{t, , } %3D

A:

Q: : If v, v1, Vz are 3 vectors in a vector space V such that v – 9vi – 3v2 = 0. Then, v belongs to…

A:

Q: 10) (6 points) Using the inner product (v, w) = 3v¡W1+5v2W2 with the vector space R?. a) Find a…

A:

Q: Suppose V₁ is a vector of all entries 1 in R" space, which we call "1-vector". What is ||v₁||2 (12…

A: Given: v1 is vector of all entries 1 in ℝn space. To find: v12 for n=16

Q: 9) Suppose {v,V,v, } is a set of linearly independent vectors of a vector space V. a) Is {v,v +v, v,…

A:

Q: If u = (3, −1, 4) and v = (−2, 3, 5), the scalar projection of y onto v is:

A:

Q: : If U, U₁, U₂ are 3 vectors in a vector space V such that v - 7v₁ + 3v₂ = 0. Then, u belongs to…

A:

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,…

A:

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

A:

Q: ): If U, U₁, U₂ are 3 vectors in a vector space V such that 13v₁ = v + 7v₂. Then, u belongs to…

A: It is provided that v, v1, v2 are three vectors in the vector space: V and 13v1=v+7v2. We need to…

Q: Let u = (– 5, – 10, – 8), v = (– 5, 6, 5), and w = (1, – 10, – 1). Prove/disprove: The set of linear…

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Q: 6. Check whether Or not F= (Osxi+CysınztSinz)i is a Coservative vector - fieid

A:

Q: Suppose that u, u and w are vectors in a real inner product space such that (u, w) = 16, (v, w) = 5,…

A: Instead of u¯,v¯,w¯ , we are writing u,v,w. (for sake of convenience). Given: (i) <u,w>=16(ii)…

Q: 3 Let W = span Given y = 1 decompose this vector into y in W and y, in w. 3 13-

A: See the detailed solution below.