Let W be the plane in R3 given by x1-2x2+2x3=0. a) Find an orthonormal basis for W b) Find an orthonormal basis for Wt. c) Write the decomposition of v=(4,3, –1)=w+w2 where wiEW and wew+. d) Find the matrix representation of the reflection operator [Refl w] that reflects a vector across the plane

Q: 14a.Show that the vectors w₁ = (0,2,0), W₂ = (3,0,3), W3 = (-4,0,4) form an orthogonal basis for R³…

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Q: Let R⁴ have a product in Euclidean. Use the Gram Schmidt process to convert the basis (u1, u2, u3,…

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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: Let W= span{(1,2,-1,0),(2,2,0,1),(1,1,-1,0)}. Use Gram Schmidt to find an orthogonal basis for W.

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

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Q: Explain how fixing a basis v1, corresponding function in n variables of the form q(x1, · ·· , Xn) =…

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Q: Consider the basis B of R² consisting of vectors Find # in R² whose coordinate vector relative to…

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Q: 5. Consider the 4 x 5 matrix A = [u₁|u2|u3|u4| u5], where the columns are U₁= 2 , U2 = 5 Uz = -1 -2…

A: The  4×5  matrix  A= u1 | u2 | u3 | u4 | u5   where  u1=1234 , u2=5102 , u3=   2-1-2   3 , u4=  1…

Q: 2. Apply the Gramm-Schmidt orthogonalization process to the vectors [1, 3, 2] and [1, 0, 1] in order…

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Q: Let V be the plane with equation 1 + 4x2 + 5x3 = 0 in R³. Find the matrix A of the orthogonal…

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Q: Let B = {V1, V2, V3, V4} be a basis of R4 given by the following vectors: 1 -2 Use the Gram-Schmidt…

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Q: Consider a physical system whose three-dimensional state space is spanned by the orthonormal basis…

A: Given Data: H^=hω03i0-i30002 ,  B^=b07i1-i-i71+i1+i1-i6,D^ =002α02α 02α0-3α

Q: - Let B = {v1, V2, V3} be the ordered basis of R3 consisting of V1 = 1 V2 = - V3 = 1 Find the…

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Q: = √1 = Let 4] 2 V2 - 2 and 3 = 2 -7 Explain that B = (V1, V2, V3) forms a basis of a 3-dimensional…

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Q: Minimize : 4yi+2y2 +y3 yi +y2 +y3 2 4 Зу1 + у2 +3уз 2 6 yi +y2 +3y3 2 5

A: For convenience we take y_1=x_1, y_2=x_2 and y_3=x_3.

Q: 1) Write v as a linear combination of the orthogonal basis V₁,...,V using dot products: V= |; V₁ =…

A: The given vectors are v=23, v1=45, v2=-54

Q: 2. Consider the following sets of vectors. Show that each set (i) contains the zero vector, (ii) is…

A: The given sets are (a) W is the set of vectors of the form 3s, -2s, s. We have to show that  i Each…

Q: Consider a physical system whose three-dimensional state space is spanned by the orthonormal basis…

A: Given Data: H^ =hω03i0-i30002 , B^ =b07i1-i-i71+i1+i1-i6D^= 002α02α02α0-3αψ0=e1ψ0e2ψ0e3ψ0=236