Let W be the set of all vectors of the form t - s Find vectors u and v in R' such that W = span {u, v} 5s – 2t

Q: Prove that for any non-zero vectors a, b, a · b = |a||b| cos(0), where 0 is an angel between a and…

A: Consider the n -dimensional vectors a and b , where n≥2 . The vectors a , b and a−b can be…

Q: Consider the set V of all vectors of the form (x y z)T where x, y and z are real numbers. 3. Show…

A:

Q: Suppose u, v and w are nonzero vectors in 3-space and a is a scalar. Which of the following are…

A: We have to choose the correct answer from the given options

Q: Find an equation of the plane that passes through the point P(4, 7, 1) and has the vector n = (1, 3,…

A:

Q: 8. Let C = 2 c=(; 1) - (;) ()- and b = Find a 2-vector z such that Cz = b.

A: we have  C=112-1b=11   we have to find a 2-vector such that  Cz=b

Q: If V is the space of all vectors in R*that are orthogonal to W = Span{(1,0,2,1), (0,0,1,5)}, then…

A:

Q: Prove that u is orthogonal to v - proju(v) for all vectors u and v in Rn, where u ≠ 0.

A:

Q: Let v be a vector of length 2. If w = -5v, u = (-2, –2) and the angle between w and u is . then v x…

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…

A:

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

A:

Q: Let W1 and W2 be skew-symmetric tensors with axial vectors w1 and w2 respectively. Show that…

A: To prove this identity we will use an identity. Proof of that identity is given below:…

Q: Let the set of non-zero vectors V1, V2,..., Vn in some vector space V be orthonormal: (Vi, V) = dij.…

A:

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: Let f(x) = sin x and g(x) = sin x + cos x  in the vector space C, [0, 2π] with the inner product…

A: The given functions are, In the vector space,

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: ): Let v = 3 be two vectors in R. and v2 %3D Show that v = belongs to span{v1, v2}. 62

A: We know that if vector "v" is linear combination of "v1" and "v2" then vector "v"belongs to the span…

Q: Let V be set of all positive real number with operations uÐv = uv for all u, v e V and cou = u° for…

A: We have V is set of positive real numbers.  We have: u⊕v=uv   for all u,v∈Vc⊙u=uc  for any scalar c…

Q: Let v1 , v2 , . . . , vn be linearly independent vectors in a vector space V. Show that v2, . . . ,…

A: If the given vectors are linearly independent in the vector space V. Then it follows that

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 for any vector u in R^n, (u^(T))*(u) = 0 if and only if u = 0.

A:

Q: Let u = (−1, 1), v = (0, 1),and w = (3, 4). Find the vector x that satisfies u−2x = x−w + 3v.

A: u=-1, 1,  v=0, 1  &  w=3, 4

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: Make all obvious simplifications.

A: We have to solve

Q: FBShow that these vectors (taken from a vector space consisting of all functions of the real…

A: The objective is to show that the vectors of the given set are not linearly independent.

Q: ^2

A:

Q: Determine all vectors v that are orthogonal to u.u = (4, −1, 0)

A:

Q: Let x 0 and y 0. (a) If xly, show that {x, y} is a linearly independ- ent set. (b) Extend the result…

A:

Q: Show that 0 x a =0 = a x 0 for any vector a in V3

A: lets take vectorv=(x,y,z) and   0=(0,0,0)

Q: 3. Use the Wronskian to determine whether the functions fi = e*,f2 sinx and f3 = x are linearly…

A: To find- Use the Wronskain to determine the functions f1 = ex, f2 = sinx and f3 = x3 are linearly…

Q: . What is the basis and dimension of the vector space: SPAN {1, cos t, cos 2t}

A:

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: Prove that two non-zero vectors u and v in n-space are perpendicular if and only if u • v = 0

A:

Q: Let v = x2 and w Y2 be vectors in R. Compute the following. %3D %3D Y3 Preview || Note: Enter x 1…

A:

Q: Let V be the first quadrant in the xy-plane; that is, let 0, a. If u and v are in V, is u + v in V ?…

A:

Q: Let u= and w- Find the unique vector v in R'such that u.v 1, v is orthogonal to w, l|v|| V3, and y>…

A:

Q: Let L be the line in R that consists of all scalar multiples of the vector 2 Find the orthogonal…

A: Concept:

Q: What is the basis and dimension of the vector space: SPAN {1, cos t, cos 2t}

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: 6. Let x#0 and y‡0. (a) If x 1 y, show that {x, y} is a linearly independ- ent set. (b) Extend the…

A:

Q: Let II be a plane passing through the origin, and let n be a non-zero vector orthogonal to II. Then…

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: Let W Span{u1, u2, u3}. Write y as a sum of a vector in W and a vector orthogonal to W. %3D

A: Orthogonal Decomposition theorem: Let W be a subspace of ℝn. Then each y∈ℝn can be written as,…

Q: 2. Prove the following identities related to the cross product of vectors (а) (и х у)хw — (u · w)v –…

A: As per our guideline we are supposed to answer only first asked  question. Kindly repost other…

Q: Find a linear mapping G that maps [0, 1] x [0, 1] to the parallelogram in the xy-plane spanned by…

A: Given: The maps [0, 1] x [0, 1] to the parallelogram in the XY-plane spanned by the vectors (2, 3)…

Q: If V is the space of all vectors in R*that are orthogonal to W = Span{(1,0,2,1),(0,0,1,5)}, then…

A:

Q: Let T R2 R2 be a linear transfor [3] into the vector a (i) T maps vector u

A: Introduction: A linear transformation could be a operation from one vector area to a different one…

Q: Let u = -2i + 3j, v = 6i - j, w = -3i.Find specified vector ||u + v ||2 - ||u - v||2 or scaler.

A: Given vectors are  u = -2i + 3j, v = 6i - j, w = -3i.

Q: Show that (x, y) = 4x1y1-7x2Y2 for vectors x = (x1, x2) and y = (V1 Y2) in R2 defines an inner…

A:

Q: b) Show that the vector w = u – proj,u is orthogonal to proj, u

A: The expression for the vector projection of u onto v is: projvu=v·uv2v Given: u=3,4,0 and v=-2,3,-6…