A. If x and y are orthonormal vectors, then find the valne of x+ yl? - |x-yl

Q: c) Show that the vector field W(x, y, z) = (2yz+ xz – x², –2xz – yz + y?, y² – x² + z²) - - is a…

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Q: 3 Among all unit vectors u = y in R', find the one for which the sum x + 8y+ 4z is minimal.

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Q: Please help me number 6. Thanks!

A: We are given that the unit vectors x, y, z satisfies the equationTo find the relation between the…

Q: An inner product (•, ·) on R³ under which the vectors 1 Vị = 1 1 , V2 = 2 satisfy (v1, v2) = 0…

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Q: Consider tne vectors A vector W =(x,x,y) in R that simultaneously satisfies the following…

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Q: Let x, y, and z be vectors in Cn and let a and B be complex scalars. Show that a ( z, x) +B ( z,y )…

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Q: In éàch párt, đétérmine whether the set of vectors is orthogonal and whether it is orthonormal w…

A: As this is a multiple subpart question according to the Bartleby Answering rule, only first three…

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: Find the orthonormal set of vectors for the following set of vectors: W1 W2 =

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Q: (b) Suppose C is a curve of length N, and ||F|| < M, where M is some positive number. Prove that ·…

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Q: 2. Find the value of a for which the vector à = (axy – z³)î + (a – 2)x²j + (1 – a)xz²k have it's…

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Q: +5 c) Let y = n44| and u = is Span{u} and one orthogonal to u. where n=9. "t. Write y as sum of two…

A: y=nn+4 and u=n+5n-1. We have to write y as the sum of two orthogonal vectors, one is span{u} and one…

Q: 4) Suppose x and y are vectors in R". Prove a) r+ >f -x->f =4(x• y) b) If x and y are orthogonal…

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Q: Two vector fields are F = -10 ax + 20 x (y–1) ay and G = x y ax – 4 ay + z az. For the point P(2,…

A: Given vector fields are F=-10 ax +20 xy-1 ayG=2xy ax -4ay +z azPoint P =2, -3, -4

Q: [1 1 2 3 4 5 1 1 'ind the nullity, dimensions of column space and the rank of the given matric A

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Q: - Given the vector fields Å = yz az – 3x a, +x²y a, B = 3 a, – 4xy a, +y² az Petermine a unit vector…

A: Given that: A→=yzax-3xay+x2yazB→=3ax-4xyay+y2az

Q: 4. Determine whether the given vectors form a fundamental set on the interval (-0, 00). -()-. X1 =…

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Q: The circuitation of the vector field F(x, y)- (3 + xy´, 4x + xy) along the boundary of the plane…

A: The solution are next step

Q: 2. Let u e R" and v E R" be two non-zero vectors, in other words at least one component of the…

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Q: Find bases for the spans of th e vectors in the given exercises from among the vectors themselves.[2…

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Q: Let x and y are orthonormal vectors in R". Then ||x – yl| is a) 0 b) c) V2 d) 2

A: Explanation of the answer is as follows

Q: 1. Consider the vectors a = (1, 1, 1) and y = (1, 1, 3) in Rº. Compute æ x y. 2. Show that, for æ, y…

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

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Q: X/ Find The normal vector to A = 2i-3j+4K , B = i-2 j+ 5K AxB=Ñ =? ĀXB=N -3 4 = -7i-6j-K %3D - 2 Hw/…

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Q: A set of vectors {u1,... , Um} in R" is called orthonorma 1 if i = j 0 if i + j. 1 %3D U¡ · Uj

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

Q: 13. Recall that nonzero vectors u and are called collinear if there exists = a nonzero scalar a such…

A: Given data:- Nonzero vectors are u→ &amp; v→ Nonzero scalar α v→=αu→

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: Let x and y are orthonormal vectors in R". Then ||x – yl| is a) o b) c) V2 d) 2

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Q: Let Uj, U2, Uz € R³ be an orthonormal system and let f : R³ → R be differentiable. Prove that af af…

A: Given that {u1,u2,u3} be an orthonormal system in ℝ3. Let us assume that {x,y,z} be the standard…

Q: Evaluate both sides for the field- rectangular parallelepiped X = 0 and 1 Y=0 and 2 and Z=0 and 3.…

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Q: 1. Determine if the vectors e2t and e-t are linearly inde- e2t e-t pendent/dependent.

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Q: Let x and y are orthonormal vectors in R". Then ||x – y|| is a) 0 b) 1 d) 2

A: If x and y are orthonormal vector in R^n .  Then ||x-y|| is √2

Q: If v is a vector in R", and if k is any scalar, then: (a) ||v|| 20 (h) x = 0 if and only if y = 0

A: Given: v is a vector in ℝn and k is any scalar To show that  a) v≥0 b) v=0 if and only if v=0

Q: Compute the integral of ſA° · dľ°P2P1 from point P1 (2,1, -1) to P2 (8,2, -1) of the vector function…

A: We have to find the integral from point p1 TP p2.

Q: The integral of vector A= 0.25p cos(q)ap +2zaz Over the bottom of cylinder specified by 1<Zs2, p = 2…

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Q: (20) Given the vector field i = (a² – y² + 2xz)î+ (xz – ry + yz)ĵ+(2² + x²)k. Find v x ở and show…

A: Given v→=x2-y2+2xzi^+xz-xy+yzj^+z2+x2k^

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: o Let ã = (5,-2,-2) and 5= (-3, -3,0) ニ Show there ane scalars s and t so that -> sá + tb = -…

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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…

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Q: 3. For any vectors U, V and scalars a, b, prove that (a) (aU) x (bV) = ab(U x V)

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Q: When is the vector x = (3) orthogonal to the vector y = ()? You may want to go through the proof of…

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Q: The vector E = = -a, – 4as + 3a, expressed in RCS and in terms of ø is Е 3 (-сosф + 4sinф)ax +…

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Q: et w and z are orthonormal vectors in R". Then ||w + z||2 + ||w – z||2 is ) 2 b) v2 c) 1 d) 0 e) 4

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Q: 2.2.12. Prove that two nonzero vectors x, y are orthogonal if and only if |x+y[? = [æ|2 + ly/².

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Q: If x = (x1, x2)T , y = (y1, y2)T, and z = (z1, z2)T arearbitrary vectors in R2, prove that xTy = yTx

A: x = (x1, x2)T , y = (y1, y2)T are arbitrary vectors in R2 .

Q: Let W = {[x]∈ R2^ | y > or equal to 0} .             [y] (a) If u and v are vectors in W , is u + v…

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Q: Let w and z are orthonormal vectors in R". Then ||w + z||2 + ||w - z||2 is a) 2 b) vz ) 1 d) 0 V2 e)…

A: Since, w &amp; z are orthonormal, so, we have, ||w|| = ||z|| = 1 and, &lt;w,z&gt; = 0 Now, ||w+z||²…

Q: Show that the vectors (1- i, i) and (2, –1 + i) in C“ are lincarly dependent over C but linear…

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Q: 2. Let u e R™ and v E R be two non-zero vectors, in other words at least one component of the…

A: Given: Let us consider the u∈ℝm and v∈Rn are two non-zero vectors and assume A=uvT∈ℝm×n. a) Presume…