Find the coordinates of x in the ordered basis B = (a, b). %3D [2]B =

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: { 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: 3 Find the coordinate vector of a with respect to the basis B for R3. 2 1.

A: We find the coordinate vector.

Q: The coordinates of v relative to the basis C are given by [v]c = P[v]g. C-B" [v]c = P[v]s C+B -72

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Q: Find the coordinate vector of P relative to the basis S = {p1.P2,P3} %3D P1 = 1 + x + x*, pP2 = x +…

A: First I have written a short note about coordinate vector of a vector relative to a basis and then…

Q: Find the coordinate vector [x]R of x relative to the given basis B= {b,. b2, bg}.

A: Here we have to find the coordinate vector [X]B of X relative to basis B.

Q: Let p = 5x + 10x + 3. Find the coordinate vector of p relative to the following basis for P2, P1 =…

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Q: For each matrix A and ordered basis B, find [LA]8. Also, find an invert- ible matrix Q such that…

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Q: Let S = y1 be a basis of R and x = E R4. What are the coordinates of x with %3D >Y2 = respect to the…

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Q: Find the matrix A' for T relative to the basis B'. T: R2 > R2, T(x, у) 3 (x — у, 2у - х), в' %3D…

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Q: Find the coordinate vector [x]B of x relative to the given basis B= {b1, b2} 3 3 b, , b2 - 7

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Q: Suppose p= 5x?+2x +3o figure out the coor olicuate relative to the follewing basis for 29 pi =i, Pz…

A: Given p=5x2+2x+3 and basis  p1=1p2=1+xp3=1+x+x2

Q: Find the matrix A′ for T relative to the basis B′.T: R2→R2, T(x, y) = (2x − y, y − x), B′ = {(1,…

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Q: Find the matrix A' for T relative to the basis B'. T: R2 - R2, T(x, y) = (x – y, y – 4x), B' = {(1,…

A: The given transformation is Tx,y=x-y,y-4x and the basis B'1,-2,0,3.

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: Find the matrix A′ for T relative to the basis B′.T: R2→R2, T(x, y) = (5x + 4y, 4x + 5y), B′ = {(12,…

A:

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 the coordinate vector [x]; of x relative to the given basis B = {b1, b2, b3}.

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Q: Find the vector x determined by the given coordinate vector (xlg and the given basis 8.

A: In this question, we have given the Basis set of vector space and the coordinate vector [X]B. By…

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: 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: Find the vector x determined by the given coordinate vector [x]R and the given basis B. - 1 1 3 - 2…

A: To find  The vector X determined by the given coordinate vector [X]_B and the given basis B.

Q: Consider the basis B of R consisting of vectors and 3 Find a in R? whose coordinate vector relative…

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Q: Find the matrix A' for T relative to the basis B'. A' = T: R² R², T(x, y) = (x + y, 3y), B' = {(-4,…

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

Q: Find x in R2 whose coordinate vector relative to the basis B is [x]B =

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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: The set B = is a basis for R2. Find the coordinates of the vector x = -6 relative to the basis B.…

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

A:

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: Given the ordered basis B = {p1 =1– 1, P2 = 4 – 7x find [p]B, the coordinates of p = -7+ 10x with…

A: Follow next step

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

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Q: The set B = {1+t²,t +t²,1+ 2t + t?} is a basis for P2. Find the coordinate vector of p(t) = 1+ 4t +…

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Q: E Let p 8x + 4x + 3. Find the coordinate vector of p relative to the following basis for P2, Pi = 1,…

A: We have to find the coordinate vector of P.

Q: Find the matrix A′ for T relative to the basis B′.T: R2→R2, T(x, y) = (2x + y, x − 2y), B′ = {(1,…

A:

Q: Find the coordinate vector of P relative to the basis S = {p1,p2.P3} P1 = 1 + x + x², P2 = x + x²,…

A: p1=1+x+x2, p2=x+x2, p3=x2; p=3-x+9x2

Q: Find the matrix of the reflection operator with respect to the straight line x=y%3Dz (in the basis…

A: Here we have to find the matrix of the reflection operator with respect to the straight line x=y=z .

Q: Find the vector x determined by the given coordinate vector [x]g and the given basis B. -2 B = ,…

A:

Q: Let B = Note that B is a basis for R?. (You do not need to prove this. (a) Find the…

A: ANSWER :

Q: Find the vector x determined by the given coordinate vector [x]pand the given basis B. [x]g

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Q: B = is a basis for R2. Find the coordinates of the vector x = relative to the basis B. -14 [x]B |

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Q: Find the vector x determined by the given coordinate vector [x]gand the given basis B. B= , [x]g =

A:

Q: Find the coordinate vector of P relative to the basis S = {p1.P2.P3} P1 = 1 + x + x², P2 = x + x² ,…

A: p1=1+x+x2p2=x+x2p3=x2p=5-x+7x2

Q: (c) (d) spaces What is the matrix of T with respect to the standard basis of both vector What is T(2…

A: As per the question we are given the matrix form of a dual transform T* and we have to find the…

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: Find the matrix A' for T relative to the basis B'. T: R2 → R2, T(x, y) = (x + y, 5y), B' = {(-4, 1),…

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Q: (a) Find the coordinate vector of x = - with respect to the ordered basis -4

A:

Q: a) Find the coordinate vector of x = of R³. To with respect to the ordered basis *- {0-1-8} E [x] E…

A: as per the guidelines I am answering only first question (a) Let the coordinate vector of x=2-40…

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.

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.