Given the ordered basis -8 -3 B = uj U2 = 7 , U3 1 4 7 find [v]B, the coordinates of v = 22 with respect to B. 25 Ex: 5 [v]g =

Q: The set B= {2+z, 6+3z + 3z,- (23+9z + 12z*)} is a basis for P Find the coordinates of p(z) = - (73 +…

A: Coordinates

Q: Determine whether S is a basis fa S = {9 – t, t³, 6t², 2t +

A: S is the basis of P3 if the vectors are linearly independent. Therefore for the vectors to be…

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: (b) The general fact that fcu++eUn]e== c\]j + .. + ca[vn]s allows for rewriting the equation above…

A: It is an important part of statistics. It is widely used.

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: Given the ordered basis B = {ui U2 = 13 with respect to B. -12 find [v]B, the coordinates of v = Ex:…

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Q: Given the ordered basis 1 B = -1 3 , U3 u2 8 -14 find vB, the coordinates of v = -21 with respect to…

A: Since B is the basis of vector space. So there must exist scalers α,β,γ from field such that  Vector…

Q: { be a basis for R? . Find the vector æ if [æ]R =| 3 Let B 8 x = x = 6. x = x = H 00

A: Given that B=11,21 be the basis for R2. We have to find vector x if xB=23. Since, xB=23 Hence,…

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

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Q: Given the ordered basis 4 B = U2 = 5 U3 = -8 -3 7 -33 find [v]B, the coordinates of v = 57 with…

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Q: Consider the following three vectors a, b and c 10 -4|,b 5,c = 7 a = 3 Lt + 3. For which values of…

A: To find the value of t.

Q: The set {GG} B = -12 is a basis for R?. Find the coordinates of the vector i relative to the basis…

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Q: Which of the following sets of vectors is a basis for R´ Select one: а. b. c. d.

A: The basis of vector space can be determined by the number of independent vectors. If the number of…

Q: Given the basis B 1 5 if the coordinates of w relative to basis B are [w]B find w

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Q: Given the ordered basis B = {p1 = 9 + 2æ, p2 = -4 – x}, find [p]B, the coordinates of p = -39 – 9x…

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Q: Given the ordered basis -1 -8 A1 = -5 , A2 -3 3 4 A4 -5 -5 -3 A3 -1 7 44 22 with respect to B. 3…

A: According to question given :-A1=96-5-3, A2=-1-830, A3=-54-1-4, A4=-5-367The coordinate of A…

Q: 18 Given the basis B -2 1 7 7 if the coordinates of w relative to basis B are wB - 4 find w 2

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Q: Find all values of a for which the given vectors form basis for R' a? u = V = and w = a 1 2

A: given vectors u=a201 , v=0a2  and w=101 claim- find all the values of a for which the given vectors…

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: 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: Let B = (1, t + 8, (t – 1)², 4t° ) be an ordered basis for P3. Find the coordinate vector of P(t) =…

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

A: Given  that                                   B=5-1,-13 and                          C=-21,3-2 be…

Q: Determine whether the given set S of vectors is a basis for Pn(R). n=1 : S = {2-5x, 3x, 7+x}

A: To determine whether the given set S of vectors is a basis for Pn(ℝ). n=1,S={2-5x,3x,7+x}

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

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Q: Find the coordinate vector of v = [2 -7 7] relative to the ordered basis B = ( [1 0 1], [0 1 1], [2…

A: ANSWER:

Q: The set B = {1 – t2, t – t², 2 – t + t²} is a basis for P2. Find the coordinate vector of p(t) = 1+…

A: The coordinate vector of p(t) relative to B will be [p(t)]B

Q: Given v = - 7i + 5j and w= -i+j, a. Find projwv. b. Decompose v into two vectors v, and v2, where v,…

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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: The vectors v.= span R but do not form a basis. Find two different ways to express -3 - 3 as a…

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Q: Find the coordinate vector of A with respect to the basis = {E22, E21, E 12 E11} of M22

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Q: The set B = {3x² – 4, 152² – (20 + 2x), 38 + 4x – 27x²} is a basis for P. Find the coordinates of…

A: Given, the set B=3x2-4,15x2-20+2x,38+4x-27x2 is a basis for P2. We have to find the coordinates…

Q: The set B = {1+tť,-t+t,1-2t+t} is a basis for P2. Find the coordinate vector of p(t) =3- 3t + 8t…

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Q: Given the basis B = the basisi B | {Q.B]} Find the change of coordinates matrix from the standard…

A: We find required matrix.

Q: Which of the following sets of vectors is a basis for R. Select one: a. b. d. EN

A: We have to find basis of R2.

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: Which of the following sets of vectors is a basis for R?? {}E} 2

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Q: 3. Given the two ordered bases U, V below for R³ (also the standard basis E = [e1, €2, €3]) (): 1…

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Q: Given the vectors V1 = (x, 1,1), V2 = (1, x, 1) and V3 = (1,1, x). S = { V1, V2, V3} of the set Find…

A: 3 vectors form a basis of R3, if they are linearly Independent. Vectors are linearly Independent if…

Q: Given the ordered basis 9. B = { u1 1,u2 , U3 = 8 -3 22 find [v]B. the coordinates of v = -15 with…

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Q: In R3, let S be the set of vectors 3 S = {V1, V2, V3, V4} = -3 -2 -4 -4 a. Explain why S spans R³…

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Q: Determine which of the given subsets form a basis for P2 . Express 5t 2 − 3t + 8 as a linear…

A: Let us consider the following set of vectors: {t 2 + t , t 2 , t 2 + 1} Let us consider the…

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

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: Consider the basis 3 3 6. B = 1 4 2 3 ,then v is the vector 3 of R. If [v]B =

A: Basis of a vector space is the linearly independent set which spans the vector space.

Q: 3. 1 V=R , cat d2= d3=1 1. 2. Tet it be Shaw that basis. Find the Ed1,22,233 in V is a Dual bose at…

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Q: [7 2 4 6 What is [A]B, the coordinates of A = with respect to the standard 10 0 1 basis B = of R2x2?…

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Q: Given the set S = {M1, M2, M3, M4}, where 3 1 2 M1 = M2 2 4 1 -3 0 -2 1 1 M3 M4 4 1 2 -1 (a) Show…

A: We will find out the required solution.