Dim (3) Ex. consider T: IR ³ -> R² T( 9₁, 92, ₁₁, 95) = (artastas, 92-94)}. T NCT) = ((a., 92, 93, 94, 95) € R² | au+as+as=0 } 92-94-0 1-D²

Q: Find the coordinates of the vector v = (7,4) with respect to the basis U₁ = (2, 1) and u₂ = (3,1).

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Q: The set B = {1-1², 2t-12², 1-1-1²) is a basis for P2. Find the coordinate vector of p(t) = 3 +…

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Q: Find a basis for the plane 4 + 3y + 5z = 0 in R. %3D

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Q: Consider the vector v = 1 + 4t in terms of the standard basis for P2, {1, t, t²} and new basis B =…

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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: 3. Let A be a n x n matrix with distinct and positive eigenvalues. For each i, 1 ≤ i ≤n, let v, be…

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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: Find an orthonormal basis of the plane z1 + 7z2 - 13 = 0. {

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Q: a' Find the value of a for which S forms a basis for R3.

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Q: Let B = {1+t, t – t2, 2t + t2} be a basis for P2. Find [-3+t – t°]B. %3D

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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: 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 p1(t) = t and p2(t) = t + 1 be polynomials in P3. (a) Show that p1(t) and p2(t)} are linearly…

A: Given: p1t=tp2t=t+1 (a) We have to show that p1t and p2t is linearly independent. (b) We have to…

Q: Find the matrix of T(ax² +bx +c) =(a-b)x² +2cx with respect to the basis {x*,x,1} of P,. Use the…

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Q: Find the coordinate vector [x] of x relative to the given basis B= (b₁,b2, b3 1 b1 = 0 B 2 b2 = 1 6…

A: here we have to find the coordinate vector of x

Q: Let p₁ (t) = 7+t², P₂ (t)=t-2t², P3(t) = 2+t-4t². Complete parts (a) and (b) below. a. Use…

A: The polynomials p1t, p2t and p3t belongs to the vector space P2 because P2 contains all the…

Q: {} Find in R² whose coordinate vector relative to the basis B is [x]B Let B = x = 12 -5 -6 [:] 5

A: Introduction: The coordinate vector of an element of vector space related to basis is the vector…

Q: 1. Find the coordinates of vector w (1,2, 3) in the basis A which consists of T1 = (1, 1, 0), 72 =…

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Q: Find the matrix A' for T relative to the basis B'. T: R2 - R2, T(x, y) = (-8x + y, 8x – y), B' =…

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Q: Let U = p E 4 (R): 1 -1 p = 0}. Find a basis of U.

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Q: Find the coordinates of (2, 3, 4, – 1) with respect to the basis B = {(1, 1, 1, 2), (1, –1, 0, 0),…

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Q: 5 Find w if (w)s = |0| relative to the basis S = {-3 -5 2 } 2 3 w =

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Q: V1 || The vectors 2 -5 O " V₂ = -5 2 7 form a basis for R³ if and only if k# and V3 = -16 -2 B k

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Q: The set B = {1+t², -t+t², 1+2t+t²} is a basis for P₂. Find the coordinate vector of p(t) = 5-6t+13t²…

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Q: A basis of R² is given as B₁ = {x₁ = (1,1), x₁ = (1,0) }; Find the change of basis matrix P, from…

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Q: (d) What is the nullity of [T]? (e) Give a basis for the kernel of T.

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Q: 1 17. В %3D is an ordered basis of R². = , 2 find x. 3 (a) If the B-coordinate vector of a vector x…

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