Let Find an orthonormal basis of the row space of A. A = 1 4 1.[C ]]}.

Q: Let B = {B]. A} mation x→→ Ax. =[%] be a basis for R2 and A = Find the B-matrix for the transfor-

A: Given that The transformation is

Q: Let W be the set of all vectors of the form 4r3s+t 2s 2r t - - 4s 2r 3t - - - (r+5s) with r, s and t…

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Q: Let W = } t s,t e R -S - 31 5) Show that -6 is in W+. 3 6) Find a basis for W+.

A: given W=s+3tt-s-t  , s t ∈R

Q: Let 9. A = 3 9 4 6. -3 2 -2 Find an orthonormal basis of the kernel of A.

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Q: Show that the set is an orthonormal basis for R3.

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Q: Let A € Mnxn (R), & be the standard basis for R", and B = {₁,...,n} be another basis for R". If P is…

A: Given, a matrixA∈Mn×n(ℝ). Given, ε as the standard basis ofℝn and  β={v1,v2,...,vn} as another basis…

Q: Let B = vector of 7 = E [V]B 0 1 00 {[%] [83] [28] [89]} 9 9 relative to B. -5 -2 || be an ordered…

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Q: 4. Present the standard basis vectors e, and ez in R? as linear combinations of (3, 1) and (1, 3).

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Q: Let S = {V1, V2} be a basis of R? where v1 and v2 = -3 What element of R? is determined by the…

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Q: 3. Find a basis for the set of vectors in R³ in the plane x + 2y + z = 0.

A: Given equation of plane is: x+2y+z=0 To find: A basis for the set of vectors in ℝ3 in the given…

Q: Let Find an orthonormal basis of the column space of A. [1 A = 2 0 -4 -4 2 4 18 .

A: Solution is given below

Q: 5. Consider the space {) a a + b+c= d : 2a + b = d a + b+ 3c = 0 H = CRª. C d (a) Find a matrix A…

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Q: Let B be the basis of R? consisting of the vectors and let C be the basis consisting of Find a…

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Q: 2. Let B = {V₁,..., Vn} be a subset of Fn containing n distinct vectors and let A = [v₁... Vn] be…

A: Let B = {v1,..., vn} be a subset of Fn containing n distinct vectors and let A = [v1, v2,... vn] be…

Q: Let Find an orthonormal basis of the column space of A. A = [115] 26 2 [270]

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Q: 8. Let W = Span{v1, v2}. Find an orthonormal basis for W. Vị = -2 , V1 = 4 2

A: An orthonormal basis for an inner product space V with finite dimension is a basis for V whose…