Show that (u₁, U₂, U3) is an orthogonal basis for R³. Then express x as a linear combination of the u's. U₁ = 2 -2.4₂ = 0 3 43 = 1 and x = 4 1

Q: Find the coordinates of the vector v = (7,4) with respect to the basis U₁ = (2, 1) and u₂ = (3,1).

A: The answer is given below:

Q: Let B = matrix from B to C 8 - { }], ] } and c-{[7], [43]} C = be two bases for R². Find the change…

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Q: Show that {u,, u2, uz) is an orthogonal basis for R. Then express x as a linear combination of the…

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Q: "Write x as the sum of two vectors, one in Span (u,.u₂.3), and one in Span (U4). Assume that (u) is…

A: In this question , we will write the 'x' as linear combination of remaining vectors .

Q: Find an orthonormal basis of the plane z1 + 7z2 - 13 = 0. {

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Q: Let B = {(1, 1, 1), (1, 5, -3), (2, 2, 1)}. Show that B is a basis for R'. For the given %3D vector…

A: To solve the following, we use the standered result of basis and spanning set Basis- Let V is any…

Q: Verify that the vectors (1,0,1), (1,1,-1), es= e₂ = form an orthonormal basis (ONB), and compute the…

A: Given vectors are  .We have to show that these form a orthonormal basis for inner product space…

Q: The vectors v1, v2 and v3 form an orthonormal basis for R3 where v1:=vector([0,0,-1]);…

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Q: Let a= and b= Show that there are scalars s and t so that sa+tb=. s = ? t = ?

A: a=-5,0,-3 and b=4,0,2sa+tb=27,0,15

Q: Let B, D be the following two bases of R³: -1 B = D= a) Find the change of coordinates matrix Po-s…

A: Solution is below.

Q: For vectors, v0= (0,3,4,2),v1= (1,1,2,1), v2= (1,0,0,0), v3= (0,0,1,0), find an orthonormal basis,…

A: Solution by using Gram Schmidt process as follows :

Q: Let B = (1, x, x², x³) be an ordered basis for P3. Find the coordinate vector 8x³ + 2x²7x - 9…

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Q: #7. Given that the three 3-dimensional vectors v1 = (- 1,3, - 4), v2 = (3, – 8, 10), v3 = (2, – 9,7)…

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Q: Expand x = (a, b, c, d) with respect to the orthogonal basis of: 2 -1 1 Vị = V2 -2 3 Express your…

A: Note: Observe that the given orthogonal basis spans only two dimension subspace of ℝ4, therefore the…

Q: Find the coordinate vector for w relative to the basis S= {u1, u2} for R2. uj = (1, 0), u2= (0, 1);…

A: Here we use basic defnition of change of basis coordinate

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: The vector x = H vector [2]8 = [2] A 1 B2 C3 in R² relative to the orthogonal basis B = What is the…

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Q: Find the decomposition of a(t) into tangential and normal components at the point indicated. r(t) =…

A: Given a position vector rt=3-t , t+5 , t2 , t=2. To Find : Decomposition of atin terms of tangential…