Let V = R°. Let B = {(1,1, 1), (1, 2, 1), (–1, 1, 0)}. (a) Express (x, y, z) as a linear combination of vectors in B. (b) Use (a) to deduce that B is a basis of V. (C) Suppose that T : R³ → R² is a linear map so that T(1, 1, 1) = (2, 1), T(1, 2, 1) =(-1,3), T(-1,1,0) = (1, –1). Find T(r, y, z). (Hint: Use linearity and (a).)

Q: Consider the vectors u₁ = [1,0,-1], u2 = [1,0,0] and u3 = [0, 1,1], v= [5, 1,3] and w= [1,0,3]. (a)…

A: As per guidelines of Bartleby i am supposed to solve on first three part,if you want more solution…

Q: 1. Consider the pointsS= (1,−3) andT= (2,5).(a) Sketch the vector−→ST.(b) Give the component form…

A: Here 2 different problems are provided. As per our Bartleby Guidelines, we are supposed to…

Q: Find the coordinate vector of p relative to the basis S = {p1, P2, P3 } for P2. p = 2 – 3x + 2x² ;…

A: Question from linear algebra.

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 V1 = 1 v2 = V3 = and y = 4 Let W = span {V₁, V2, V3}. Find the orthogonal projection of the…

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Q: Let u = (-1,0,1), v= (3,2,1) and w= (0,1,2). (b) Prove that the vectors u v and w are linearly…

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Q: Let x = (1, 1, 1, 1)T and y = (8, 2, 2, 0)T . Verify that x − p is orthogonal to p.

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Q: 1a. Given vectors v₁ = (1, 0, 0) and v₂ : (1, 0, 0) and v₂ = (0, 1, 0) in R³, find a vector V3 such…

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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 coordinate vector [x]R of x relative to the given basis B= {b1, b2, b3}. 1 4 1 - 6 b, 0 ,…

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Q: (3) Let L be the line y 2r in the plane. Find a matrix C such hat for every vector H plane, the…

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Q: Find the coordinate vector for w relative to the basis S= {u1, u2} for R2. uj = (1, 0), u2= (0, 1);…

A: Here we use basic defnition of change of basis coordinate

Q: Let u = (-1,0,1), v= (3,2, 1) and w = (0,1, 2) . (a) Prove that the vectors u – v, u+ v and u x v…

A: Given : u=<-1,0,1> v=<3,2,1> w=<0,1,2>

Q: A jungle has 400 monkeys, and it is estimated that the maximum population of the monkeys in the…

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Q: H [3t-2] t+3 [2t-3] (a) Find all values of t for which w and z are orthogonal. 2. Consider the…

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Q: The vector x = H vector [2]8 = [2] A 1 B2 C3 in R² relative to the orthogonal basis B = What is the…

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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.