What is [v]B, the coordinates of v = with respect to the standard basis B : of R?? Ex: 5 : [v]B =

Q: In Exercises 13–16, define T : R² –→ R² by T(x) = Ax. Find a basis B for R? with the property that…

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Q: Given the ordered basis B - {m = ["] = {u1 , U2 find [v]g. the coordinates of v = with respect to B.…

A: Let β= u1 , u2 , ...... , un    be an ordered basis for a finite dimensional vector space V. For x ∈…

Q: What is the basis and dimension of M3(R)?

A: Basis: For a vector space V, the set of linearly independent vectors that generate the whole vector…

Q: Suppose v1, ..., V, are nonzero, mutually orthogonal vectors in R". a. Prove that they form a basis…

A: A set v1,v2,…,vn is a basis for a space V if every element in the space V can be written as a finite…

Q: Consider the following vectors. 6, us Apply Gram-Schmidt to find an orthogonal basis for S. (a) S =…

A: a) S=spanu1,u2 orthogonal basis for s=w1,w2w1=u1=4-10w2=u2-u2,w1w1,w1w1     =381-12-8+016+1+04-10…

Q: b) Using the basis S in (a), find [T)s if ū = (2, i, 2 – i).

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Q: Find the coordinate vector [p(x)]B of p(x) = x² + 4x + 4 with respect to the basis B = {x³ + x – 2,…

A: According to the given information, it is required to find the coordinate vector.

Q: Compute  the  coordinate  vector  of  v with  respect  to  given ordered  basis  S  for  V . V is P1…

A: Given: v→=t+4 Ordered basis for v→ :  S = {t + 1, t − 2}

Q: Let QE M,(R) be given such that the columns of Q form an orthonormal basis for R". Prove that Q'Q =…

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Q: Find an algebraic description of the range of A by row reducing A^T and using the relation between…

A: We know that rank(A) = rank(AT). We need to find an algebraic description of the range of A by row…

Q: Consider the basis B of R consisting of vectors and Find x in R whose coordinate vector relative to…

A: Basis is defined as the linearly independent set that span a vector space V. Any vector of V can be…

Q: Given the ordered basis B , U2 5 find (v]B, the coordinates of v : with respect to B. Ex: 5 (v]s

A: Given: and Notice that v=u1. So, it can be observed that v=u1+0u2.

Q: Find a basis fo

A: Given,            A=3-916-26-161-38

Q: Given the bas is x, cwhere X= X,J for R3 2. 3. use the Gram - Schmidt process to transform the basie…

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Q: Given the following three vectors: Show that v1, v2, iz form a basis of R by proving that they are…

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Q: find the matna X for T elative to the basis B: T:R'R*, TG j) = (x-J,y-ta), 8'-{(1, -), CO 3)} I D

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Q: Define T:R?→R? by T(x) = Ax. Find a basis B for R with the property that [T]B is diagonal. 2 - 4 A =…

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Q: {( a + b+c+d b – c+ 2d а + 2с — d H = : a, b, c, d e R } C R³, and consider --(}) u = 1 (а) Is u E…

A: Given, H=a+b+c+db-c+2da+2c-d: a,b,c,d∈ℝ⊆ℝ3      ⋯⋯(1) a) Given, u=111 Consider the system,…

Q: Given the following vectors, let W Span{v, v2, vs}. v3 (a) ( . Is z in W? Why or why not? (b) ( Find…

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Q: Q. If B = {e, = the usual basis R2. Determine its dual basis. ?? ده رده را( = (D, 1)} is

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Q: Let TilP > Pz, the basis of NIT) T (ax²+bx+c) = 2Qx+ b. Then %3D is

A: Applying nullity definition we have

Q: Show that {e1,€2, - } is a Schauder basis for P, 1<p< ∞, where S1 ifi=n (E") en = %3D 0ifi#n.

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Q: 3) li) Find the dual basis {l, l} of the standard basis of IR". (i) Fiod th

A: Since you have asked more than one question, we will solve first one for you. If you want other…

Q: What is [A]B, the coordinates of A = | 3 with respect to the standard 8 1 0 0 1 basis B of R2x2? 0 0…

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Q: Suppose R* = is a basis for R*. Span {v1,..., V4}. Explain why {V1,...,V4} %3D

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Explain why S is not a basis for P2.S = {−x, 4x2}

A: Given: S={−x, 4x2} To Explain: Why S is not a basis of P2.

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: Let Pa represents multiplication by 1+t? with respect to the basis B = {1,t,ť²} for P2 and BU{t,t*}…

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Q: Show that the following set of vectors is a basis for M22: 5. 3 12 - 4 Let V be the space spanned by…

A: As per the guidelines I am supposed to do the first question among multiple questions. So I am…

Q: and ŷ = Find the values of y, and y, such that vectors = constitute an orthonorma L0.8337! basis in…

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Q: Let W = {ax? + (b-a)x + (a+b)| a, b e R}. Find a basis for V and find the coordinate vector for v =…

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Q: Let TiPe s Pe, T(ax?+ bx+c) = 2Qx+ b. Then the basis of NIT)

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Q: Define a basis v1, v2 of R² by vị obtained by applying the Gram-Schmidt Procedure to v1, v2? 2 by…

A: Consider the provided question, A Basis of a vector space. Let V be a subspace of Rn for some n. A…

Q: Given the ordered basis -5 B uj = U2 = 13 with respect to B. -12 find [v]B, the coordinates of v =…

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Q: Let TilPe ~> Pe, Tlax?+bx+c) = 2QX+ b %3D the basis of NIT) is True False

A: Applying nullity we have

Q: Are the following vectors a basis for P ? Explain why or why not. v = 1+ x? + x, = 1- x, vz = 1+ x +…

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Q: What is [p]B, the coordinates of p = 4+ 7x with respect to the standard basis B = {1, x} of P1? Ex:…

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Q: Let x and y be nonzero vectors in Rm and Rn,respectively, and let A = xyT .(a) Show that {x} is a…

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Q: Explain why S is not a basis for P,. S = {1 – x, 1 – x², -1 – 6x + 7x2} || O sis linearly dependent.…

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Q: .Let W = {ax? + (b-a)x + (a+b)| a, be R}. Find a basis for V and find the coordinate vector for v =…

A: find basis of V then will find coordinate

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Q: In P, consider the basis B- {6,6} where 1 %23 b2 I – 4 Task Find the coordinates of vector w = 2z +…

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Q: 23. Suppose R* = Span {v1, ..., V4}. Explain why {v1,..., V4} is a basis for R4.

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Q: Find x with respect to the standard basis corresponding to the coordinate vector [x]; and basis B. 4…

A: B ={b1,b2,b3} [X]B = {x1,x2,x3} Then X =x1.b1+x2.b2+x3.b3

Q: O Find Hhe mahix A for T relative to the basis 8, where B' is made up of the baris vertors fand in…

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Q: Let B={ }].OH} be basis for IR %3D Find [v]o where 6- 563

A: Given β=3-30,22-1,114 be basis for ℝ3 v=15-93 To find vβ

Q: Explain why S is not a basis for P,. S = {1 – x, 1 – x2, -1 – 7x + 8x²} O sis linearly dependent. O…

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Q: Let TilPe > Pz , T (ax?+bx+c) = 2Qx+ b. Then the basis of NIT) is

A: Just use a definition of Nullity of transformation.

Q: Show that the given vectors form an ortho­gonal basis for R2 or R3• Give the coordinate vector [w]of…

A: Orthogonal basis:        Let v1,v2,.....,vn be linearly independent vectors in Rn, if v1,v2,.....,vn…

Q: thogonal basis for W:

A: Orthogonal decomposition of vector