Let z= y- 4a, a u'v and y-v- 3u. Compute On kum)-(1,1) -

Q: calculate v × w.v = v = (1, 1, 0), w = (0, 1, 1)

A: Given v=<1,1,0> and w=<0,1,1> v×w=i→j→k→110011         =i→(1-0)-j→(1-0)+k→(1-0)…

Q: 4. Let V1 = (-3) - () -- () 5 = V2 10 V3 = " 12 a) For what values of h is v3 in Span {V₁, V₂} ? b)…

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Q: Let u = (3, 2, x) and v = (2x, 4, x). (a) Find all possible values of x that make u and v…

A: Given thata)We have to find all possible values of x that make u and v orthogonal.b)We have to find…

Q: Q3. a) Express the vector (4,2) e R' as linear combination of the vectors (1,1) and (1,-1). b) Let T…

A: We have to find all these

Q: Find the projection of u = onto v = .

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Q: Calculate the cross product assuming that u x w = (6, 3, 6) (-u+3w) x w =

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Q: 8.) Find a vectorx such that 5x-2v=2(u-5x) SOLUTION

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Q: Compute u X v.

A: Here given vector as u=3-12, v=011 These vectors can be written as u=3i-j+2kv=j+k

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: Find scalars x, y and z such that x(2, 1, 4) + y(1,−1, 3) + z(3, 2, 5) = (6,11,6)

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Q: Let T (V₁, V2, V3) w = (4, 1, −1). = (2v1 + V2, 2v2 − 3v₁, V₁ — V3). Find T(–4,5,1) and pre-image of

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Q: Express the Vector x as a linear combination of the U's U₁ Gl , 02 [1] ·16

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Q: Show that u1 =(2,1,1) u2= (-2,2,1) u3= (1,-1,-2) are linearly dependent show all working and explain…

A: Given :u1 =(2,1,1) u2= (-2,2,1) u3= (1,-1,-2)

Q: Calculate 121x dxdy where R is the parallelogram with vertices (0,0), (6,2), (7,6) R 1 -(v — Зи), у…

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Q: Find the projection of u onto v if u= (5,-3), v = (-1,4).

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Q: (-9,6) Use matrices to reflect the vector the line y = x. ove

A: Topic:- algebra

Q: 2 Locate the numbers z₁+z₂ and z, - z₂ vectorially when z₁ = 2i, z₂ ==-i. 3

A: Use addition the evaluate these numbers then plot it

Q: Given u, v and w from question 3, find (a) the angle between u and w,

A: u = (4,0,-2) and w = (2,1,6)

Q: Find a and b such that v-au bw, nhere u-(1, 2) and w- (1. -1) v - (4, 5)

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Q: Suppose that r1(t) and r2(t) are vector-valued functions in 2-space. Explain why solving the…

A: Given- r1t and r2t are vector - valued function in 2-space. To explain equation r1t=r2t may not…

Q: In the questions below determine whether the set is finite or infinite. If the set is finite, find…

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Q: Find the projection projuv, where u = (1,3,-2) and v = (2,-1,3).

A: Since we kow that the projection of v on u is given by                projuv=u.v||u||2u

Q: 6. Show that the vectors (1,1,0), (1, 0, 1), and (0,1,1) generate F3.

A: In this question, we will show that the given vectors generate F3 .

Q: (2) Let aj = (1,2, -1), a2 = (3,0, 1) and bị = (-1, 10, 7), b2 = (1, 2, 0) in R³. %3D (a) Is a, in…

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Q: Find u. (v x w). (6, 6, 6) (1, 7, 0) - (0, 0, 1) > 3

A: Given that,u=6,6,6v=1,7,0w=0,0,1