Let B = {1, x, x², x*} be an ordered basis for P3. Find the coordinate vector of f(x) = 4x3 – 72² + 8x – 6 relative to B. fB =

Q: Let β = { u1, u2, .. . , un} be a subset of Fn containing n distinct vectors, and let B be the…

A: Given that, β=u1,u2,...,un is a subset of Fn and let…

Q: i) Find the matrix of T with respect to ordered basis B' = {(1, 1), (1, – 1);:.

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Q: 4 Let A = and define T : R? → R? by T(x) = Ax. Find a -2 -1 basis B such that the matrix [T]s is…

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Q: Given the coordinate matrix of x relative to a (nonstandard) basis B for R", find the coordinate…

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Q: Let B = (1, x + 8, (x – 1)², 5x³) be an ordered basis for P3. Find the coordinate vector of %3D f(x)…

A: We have used the standard basis C {1,x,x^2,x^3} to write the coordinate vectors for f and each…

Q: Given the basis {x,, X, cohere X,= 「に XgJ for R3 2 3. use the Gram - Schmidt process tO transform…

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Q: Given the coordinate matrix of x relative to a (nonstandard) basis B for R", find the coordinate…

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Q: Find the coordinate vector of p (x) = 1 + 2x + 3x2   with respect to the basis ẞ = {l + x, 1 -x, x2}…

A: Here given

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: Let B be the standard basis of P₁, and consider the basis B' [T]B¹,B. = {(1)· (9)}< of V. Find

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Q: Explain why S i not a basis for P2. S = {1, 4x, -5 + x?, 3x} O sis linearly dependent. O s does not…

A: We have to find out

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

A: here we have to find the x with respect to the standard basis corresponding to the coordinate vector…

Q: Prove that the components of a vector x in a given basis {ê¿} are unique. That is, show that if you…

A: We will prove the given statement.

Q: Find the coordinate vector of x2 + x - 17 relative to the basis {x² + 1, x + 2, x - 3}.

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Q: Let B be the basis of R² consisting of the vectors and let C be the basis consisting of Find a…

A: Solution:-

Q: Let B = (1, x, x², x*) be an ordered basis for P3. Find the coordinate vector of 8x – 6x2 – 9x + 3…

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Q: Let B be the basis of R? consisting of the vectors 4 -2 and let C be the basis consisting of 3 2…

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Q: Given the coordinate matrix of x relative to a (nonstandard) basis B for R", find the coordinate…

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Q: Q1:Find an orthonormal basis for the Euclidean space R* that contains the vectors U1 uz = and uz

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Q: 2

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Q: 3) Let S contain vectors of the form f(x) = a + bx + cx² + dx³ : f(-2) = 0 and f'(-4)= 0: Then a…

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Q: Let B be the basis of P2 consisting of the Laguerre polynomials 1, 1 -t, 2 – 4t + t2, and let p(t) =…

A: Let β=1,1-t,2-4t+t2 be the basis for P2R For Pt∈P2R , can be written as linear combination of…

Q: Find the coordinate vector of p(x) = 3 - x + 4x2 with respect to the basis B = {1, 1 + x, -1 + x2}…

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Q: (a) Find the coordinate vector of æ with respect to the ordered basis E = -2 of R3:

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Q: Let B = (1, x, x², x³) be an ordered basis for P3. Find the coordinate vector of f(x) = - 823 6x? –…

A: ANSWER :

Q: Given the coordinate matrix of x relative to a (nonstandard) basis B for R", find the coordinate…

A: Let the given vectors be u=(1,0,1), v=(1,1,0)  and w=(0,1,1) So, we have B=u,v,w  and xB=231 The…

Q: What is the coordinate vector for the polynomial p(x) = 2 – x² + x'relative to the standard basis…

A: our objective is to find the coordinate vector for the polynomial p(x).

Q: Given the coordinate matrix of x relative to a (nonstandard) basis B for R", find the coordinate…

A: Here, B=0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1 is a non-standard basis for Rnand the…

Q: 4. Let {V1, ... , Vn} be an orthogonal basis of R". For any vectors x, y in R" show that Σ (х - V,)…

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Q: Let P2 denote the vector space of all polynomials in the variable a of degree less than or equal to…

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

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Q: Find the matrix A' for T relative to the basis B'. T: R2 > R2, T(x, у) 3D (4х — Зу, 5х), В' %3 {(-2,…

A: Tx,y=4x-3y,5x

Q: Find an orthogonal basis for R3 that contains the vector

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Q: Find x with respect to the standard basis corresponding to the coordinate vector [x]g and basis B. 2…

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Q: Given the coordinate matrix of x relative to a (nonstandard) basis B for R", find the coordinate…

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Q: (a) Show that {v1, v2, V3} are linearly independent, where 1 V1 = 1 and v2 = and v3 = -2 Hence {v1,…

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Q: A is a 3 x 5 matrix and (v1, v2) is a basis of null(A). The vectors v3, v4, vz E R³ satisfy Avz =…

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Q: Find the matrix A' for T relative to the basis B'. T: R2 - R2, T(x, y) = (x - 3y, 2x), B' = {(-2,…

A: Here we have to find out matrix for the given linear transformation.

Q: Given the coordinate matrix of x relative to a (nonstandard) basis B for R", find the coordinate…

A: Here we have to change the coordinates of x from given basis B to standard basis S.

Q: Let B (1, x + 3, (x – 1)², 5æ³ ) be an ordered basis for P3. Find the coordinate vector of f(x) =…

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Q: Let {u₁, U2, u2} be an orthonormal basis for an inner product space V. Suppose v = au₁ + bu₂ + cuz…

A: We have v=au1+bu2 +cu3 Now, ∥v∥=a2+b2+c2 Given ∥v∥=80 So,  80=a2+b2+c2⇒802=a2+b2+c2⇒80=a2+b2+c2…

Q: In the vector space f, of polynomials of degree at most two, the third column of the matrix of…

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Q: i) Find the matrix of T with respect to ordered basis B' = {(1, 1), (1, – 1)} %3|

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Q: 3 Find the coordinate vector of x = -2 with respect to the basis B for R3. -2 6 ||

A: Given that the vector x→=3-2-2 and the basis is 166,01-5,001. It is required to find the coordinate…

Q: Explain why S is not a basis for P2. S = {1 – x, 1 – x², -1 – 6x + 7x²} O sis linearly dependent.

A: Given that S=1-x,1-x2,-1-6x+7x2 Explain why S is not a basis for P2 if S is linearly dependent the S…

Q: Let {f1, f2, f3} be the dual basis of {e1, €2, €3} for R³, where e₁ = (1, 1, 1), €₂=(1,1,−1), Find…

A: Given basis are e1,e2,e3 of R3 where e1=1,1,1e2=1,1,-1e3=1,-1,-1 Its dual basis are f1,f2,f3 We have…

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

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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: Suppose T E L(V, W), and w1, ..., wm is a basis of range T.

A: Given that T∈L(V,W)andw1,.......wm is a basis of range T.To prove there exist…

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.