Express the following as a linear combination of u= (3, 1, 7), v = (1, -1, 7) and w = (6, 3, 6). (13, 8, 13) = i u- v+

Q: Q5. Are the set of vectors {[0 2 1]",[1 1 1]", [3 2 1]", [3 0 1]"} linearly independent? Does the…

A: Set of vectors are linearly independent if there is no non-zero solution of c1,c2,c3,c4. If there is…

Q: Show that the vector a=(-1,13, – 5)can be written as a linear combination of b = (1, 4, – 2) and c=…

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Q: Determine D„f(4, –1,6) for f(x,y,z) = ex³y + 4zx³ in the direction of (–3,2,6). %3D

A: Given that fx,y,z=ex2y+4zx3 Then  ∇f=∂∂xi+∂∂yj+∂∂zkex2y+4zx3=2xyex2y+12zx2i+x2ex2yj+4x3k

Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

A: we have to find the vector in linear combination form

Q: Find the component of u along v. u - (-2, 4), v- (1//7, 1/v2)

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Q: А Q(1, 1) в Q(2, 0) vyQ(1, y) 3xQ(x, 2)

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Q: (d) u =-,v = xy, = a' ху, 21

A: Consider the given information. (d) Consider the given values. u=12-12x2v=xy The equation of the…

Q: Write v as a linear combination of u and w, if possible, where u = (1, 2) and w = (1, −1). v = (−1,…

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Q: Find the best approximation to u = (3,-7, 2, 3) as a linear combination = (2,-1,-3. 1) and =…

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Q: 5. i ',, Find the solution space and write it as a linear combination of vectors. - x3 + 5x4 X2 +…

A: Given that x1-x3+5x4=0 x2+4x3-3x4=0

Q: T: R2 R2 is defined by х + 7х, [3x, – 4x2] X1 %3D and B = {u,,u,} and B' = {v,v,}, where %3D -- --…

A: Given transformation T:R2→R2, defined by Tx1x2=x1+7x23x1-4x2 and B=u1, u2 and B'=v1,v2 Here u1=22,…

Q: In each case, find the linear combination of the first two vectors that is as close as possible to…

A: Both part of the question can be converted into the question based on least squares solution of a…

Q: If {v1, v2, . . . , vn} is a linearly dependent set of vectors, prove thatone of these vectors is a…

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Q: Find ||u||, ||v ||, and ||u + v||. -(-1. 금), v-(2.-3) v = (2 - ± ) u = 4 (a) ||u|| (b) ||v|| (c) ||u…

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Q: - Show that the vectors X, - () 5e3t and X2 = ) 2et 7et form a linearly independent set.

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Q: Every vector of R²is linear combination of (-1, 1), (2, –2)? Justify

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Q: Let f(x, y, z) 75 Then Vf = and Duf(1,3, -3) in the direction of (-1, -2, -2) is

A: Given the function

Q: photo is attached

A: Given informationVector V = (-3, 5)

Q: This question is from partial differential equation please sir g give me answer immediately

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Q: Represent the line segment from P to Q by a vector-valued function. P(7, 0, 9), Q(6, −6, 7) r(t)…

A: Given: Represent the line segment from P to Q by a vector-valued function. P(7, 0, 9), Q(6, −6, 7)…

Q: Find ||u||, ||v||, and ||u + v||. u = -2, V = 5, (a) ||u|| (b) ||v|| (c) ||u + v||

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Q: Determine whether u= (-1, 11) is a linear combination of x =(1,3) and y=(2,-1).

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Q: Determine R21, the vector from P2(5, 2,–4) to P1 (3, –1,0). 2аx + Зау — 4а, — 2ах — Зау + 4a, | 4ах…

A: Given the points P25,2,-4 and P13,-1,0. To find vector R21 from above two points. The vector from…

Q: For the points A(1, 5, -7) and B(3, 0, 1) vector AB has coordinates

A: Given point A and B. Find vector AB.

Q: If u = (u, uz) and v = (V1, V2), how do you find u + v?

A: Given: u=(u1,u2)v=(v1,v2)

Q: what is the linear combination of  u⃗  and v⃗ ?

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Q: c) Show that vector ū = 1 cannot be expressed as a linear combination of 2 in R3 3 vectors vi 1 and…

A: we have to show that , we can not write as a linear combination of vectors v1 and v2

Q: Express w as a linear combination of u and v. 1 - 5 u = V: w = - 9 w = u+

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Q: If = 2 z-x'y and A = 2x'î-3 yzj +x z'k, find A.V and A xV4 at the point ( 1,-1,1).

A: given ϕ=2z-x3y and A=2xi^-3yzj^+z2 k^ find at the point 1,-1,1 1) A·∇ϕ 2) A×∇ϕ

Q: Let f(x, y, z) 48 Then Vf = and Duf(2, 1, 3) in the direction of (2, 1, 2) is

A: This is gradient of f in which take all first order partial derivatives.

Q: Find 2 (v x u), given u x v = (-, 5, 8). %3D

A: u×v=-83, 5, 8

Q: Solve for w where u = = (0, 1, 1, –1) and v = (0, -1, 2, 3). %3D 5w = u - 4v W =

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Q: If A = 2x2'i– yzj +3xz'k and ø=x³yz, find V×(ø4)at the point (1, 0, -1).

A: Given A = 2xz2i - yzj + 3xz3k and  ϕ = x2yzSo, ϕA=  x2yz(2xz2i - yzj + 3xz3k)     =  2x3yz3i…

Q: Express the vector x as a linear combination of the u's. U₁ = 0, U₂ = 5, -1.4 U3 Ox=-3u₁ +4u2 +243…

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Q: Q1) If the vectors A, B, C and D in the same plane, prove (AxB) x (CxD) =0?

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Q: Express the vector v =-1 as a linear combination of the vectors -3 0,v2 4 and v3 -4 , if possible.…

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Q: In each part, determine whether the vectors are linearly inde- pendent or are linearly dependent in…

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Q: For which value of x do the following vectors form a linearly dependent set in R V =| x, x,

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Q: Find (u, v) for (u, v) = 2u,v, +3u, v, +u,v, defined in R, where u (9,0,-3) and v (8, 2,17). A. (u,…

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Q: Write v as a linear combination of u,, u2, and uz, if possible. (If not possible, enter IMPOSSIBLE.)…

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Q: Find the component of u along v. 3(5,2), v = (3, -4)

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Q: 8. xyzx +2y³ (z, = 1

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Q: When the set of vectors {u1, u2, . . . , un} is linearly independent and the set {u1, u2, . . . ,…

A: We have given; The set of vectors {u1, u2, . . . , un} is linearly independent and the set {u1, u2,…

Q: 6. Write as a linear combination of the vectors

A: solving by linear combination of the given three vectors by converting into syatem of equation...

Q: Let S = { t² + 1, t² – 1, t – 2}. - 2. If S is linearly independent in P2, write 2t2 – t + 5 as a…

A: Three vectors A,B,C are said to be linear dependent, then there exist three numbers a,b,c such that…

Q: Determine if the vector x̄=(-12i-j-5k) can be expressed as a linear combination of ū=(1,-1,0),…

A: The solution of the problem is given in the next steps.

Q: What is the dependence on the following vectors: u=(3.0.1), v=(1,-1,0) and w=(1.0.1) thanks!

A: A set of vectors {v1,v2,...,vn} in Rn is said to be linearlyindependent if the vector equationx1v1 +…

Q: Determine Df(4, -1,6) for f(x, y,z) = ery +4zx in the direction of (-3,2,6).

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