1 3 - 1 - 3 -9 - 8 Let P = - 3 -5 ,v1 = 4 V2 = 6. and v3 = 2 Complete parts (a) and (b). 4 1 4 7 a. Find a basis (u,, u2, u3} for R° such that P is the change-of-coordinates matrix from (u,, u2, u3} to the basis (v,, v2, V3}. [Hint: What do the columns of P represent?] C+ B 8 - 4 - 5 u, = u2 = -8 , u3 = - 2 18 21 b. Find a basis (w,, w2, W3} for R such that P is the change-of-coordinates matrix from {V1, V2, V3} to (w,, W2, W3}. W, = W2 = W3 =

Q: 1 2 Consider the column vectors vị = V2 = -1 and v3 = -1 1 (a) Use row operations on an appropriate…

A: The column vectors are v1=101, v2=2-10 and v3=0-1-2

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Q: Calculate r'(t) and T(t) and evaluate T(1). r(t) = (6 + 7t,12,5 – 1²) (Give your answers using…

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Q: Consider the space P2 and consider the vectors B ={ 1 + 2t +2t2, 3+5t +3t2,-2-3t} and C = {1,t,t2}.…

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Q: Find the vector P,P2 and P2P1 P:(3.2,3) , Р.(5,7,-1) b- P1(-2,-1,0), P2(4,-5,2) a - P1(0,3,3),…

A: We can solve the given problem as follows:

Q: Three vectors (PQ), (PR), (QR) have been written in matrix form as shown below: 2 -17 PQ1 1 PR = -2…

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Q: EXAΜPLE2 Determine whether the vectors vi-(1,-2,3),v2=(5,6,-1),v3-(3,2,1) are linearly independent…

A: Given vectors are v1 = (1, -2, 3), v2 = (5, 6, -1), v3 = (3, 2, 1)

Q: Find the composed matrix for aligning a vector v along the unit vector j. Assume 3-D coordinate…

A: Given a vector v in the three dimensional coordinate system. And the unit vector j.   The component…

Q: The coordinate vector of the (-4,3,1) in the B={u= (1,1,1); v = (1,0,1); w=(0,0,1)} is : A. (-4,3,1)…

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Q: Help!! Please answer correctly

A: a)Let v=⎣⎢⎡​xyz​⎦⎥⎤​∈R3Let cB​=⎣⎢⎡​cB1​cB2​cB3​​⎦⎥⎤​ be the cordinate vector of v with respect to…

Q: The coordinate vector of the vector (-4,3,1) in the basis B = {u= (1,1,1); v = (1,0,1); w=(0,0,1) }…

A: We have to find the coordinate vector of the vector -4, 3, 1 in the basis B=u=1,1,1; v=1,0,1;…

Q: 1. Say whether the following vectors are linearly independent and whether the vectors form a basis…

A: Given Data: Let us consider the given data, c 2,-2,1,0,2,-2,2,0,-1d 1,1,1,1,-1,-1,-1,1,-1,-1,-1,1…

Q: Given three linearly independent vectors V1 = (-1,4,-2,-4,-9), V2 = (-5,4,5,0,-4), Үз %3D (1,-3,9,…

A: The solution is given as

Q: 3) Find the vector projection of A onto B. (Projs A). b\ If possible, use matrix inversion method to…

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Q: The coordinate vector of the vector (-4,3,1) in the basis B={u= (1,1,1); v = (1,0,1); w= (0,0,1) }…

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Q: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

A: Given,S = { (2, -1, 3), (5, 0, 4) }To find:  the vector as a linear combination of the vectors in S.…

Q: 2. Let V₁ a. 14 -2' b. V₂ = " 16 10 spanned by B. Note that B is an orthogonal set. -49- 35 7 -28_…

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Q: Find a set of vectors {ū, v} in R* that spans the solution set of the equations w – x 4z 0, 2w + 2x…

A: We have four unknown variables (w,x,y,z) and two equation. This emply there are two free variables.…

Q: Find a subset of the vectors that forms a basis of their span: (i) vi = (-1,1, -2,1), v2 = (2,-2,…

A: For (i), Notice that v2=2, -2, 4, -2=-2-1, 1, -2, 1=-2v1. So, the subset of the vectors that form a…

Q: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

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Q: Find the scalar and vector projections of b onto a. a = (-3, -6, 2), b = (2, 1, 1) comp b= proj₂b =

A: Given that the vectors a=-3,-6,2 b=2,1,1   .

Q: vector of the vector basis The coordinate (-4,3,1) in the B={u= (1,1,1); v= (1,0,1); w=(0,0,1) } is…

A: