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

A: The answer is given below:

Q: 1 Let C = [c1, c2, c3] = -1 2 3 -1

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Q: Determine whether the vectors (3,0, 3, 6), (6,0, 0, 3), (0,0,3,0),(6,3,9,12) form a basis of R*.

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Q: Write the vector v = B - 3 8 {[][]}· 8 -2 as a coordinate vector with respect to the basis

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Q: nd the values of the scalars a, b, c such that -2,1, –3) = a(2, -1,1) + b(1,3,–2) + c(-2,1,–3) %3D

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

A: fB​=[161, −19, −6, 4]Explanation:Detailed explanation:This is a detailed guide explaining how to…

Q: Find the coordinate vector of p relative to the basis S = {P₁, P₂, P3 } for P₂. p = 15 - 20x + 6x²:…

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Q: Consider the basis B of R² consisting of vectors (-1, 2) and (-6, -3). Find x in R² whose coordinate…

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Q: Let B = {(1, 1, 1), (1, 5, -3), (2, 2, 1)}. Show that B is a basis for R'. For the given %3D vector…

A: To solve the following, we use the standered result of basis and spanning set Basis- Let V is any…

Q: let u = 2i -5j  ;   v =-3i+7j  ;    w=-i-6j Find each specified vector of scalar A. 3w+2v b.…

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Q: Consider the space P2 and consider the vectors B ={ 1 + 2t +2t2, 3+5t +3t2,-2-3t} and C = {1,t,t2}.…

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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: Show linear dependence in part (ii) to show that ({1,0,1}) is a basis.

A: From part ii)We have to show that the set  is a basis of .We know thatA basis B of a vector space V…

Q: Find the stable vector of 1 3 4 4 P = 4 %3D 3 7

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Q: Let B = (1, x + 7, (x − 1)², 6׳) be an ordered basis for P3. Find the coordinate vector of f(x) =…

A: Given,                be an ordered basis for  and             To find the coordinate vector of…

Q: Q2) Find the coordinate vector [x]B of x relative to the basis B={b1, b2}:

A: Let us consider a vector V  with the basis b1,b2,......bn then any vector v∈V is written as linear…

Q: https://www.youtube.com/watch?v=pE5yxgmXMmQ&t=267s This video was given as a guide

A: ANSWER AND SOLUTION: To find the coordinate vector of the polynomial f(x) = −8x3 + 3x2 − 3x + 7…

Q: Rachel deposits $12,000 into a fixed asset account that earns 6% compounded quarterly. What is…

A: Formula:      where FV = Future Value          PV = The principal amount (the initial amount of…

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: Determine the basis that generates the following vector space by clearing the variable y: M = {(x,…

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Q: Write v as the sum of two vectors, one in Span fu,} and one in Span fu2,u3,u4}. Assume that fu1 .u4}…

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Q: Let F = sin(4x +3z) i-6ye*z k. Calculate div (F) and curl (F). (Express numbers in exact form. Use…

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Q: 2. Determine whether the following vectors span the vector space P₂: P₁ = 1+ 3x + 2x², P2 = 3-x+3x²,…

A: We have to determine that whether the following vectors span the vector space P2 or not : p1 =…

Q: Let B={b₁,b₂} be the basis in R2 pictured below. b₂ 0 If the coordinate vectors [11] b₁ a

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Q: Let B = (1, x, x², x³) be an ordered basis for P3. Find the coordinate vector 8x³ + 2x²7x - 9…

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Q: Determine whether the set of vectors {(2,-1,3),(4,1,2),(8,-1,8)} form a basis for R3.

A: Consider the vectors : 2,-1,3, 4,1,2, 8,-1,8 To form a basis these vectors, the vectors must be…

Q: Decide whether the vectors [2, 9, -1, 4, 7, 8, 10, 9], [11, 2, 5, -9, 0, 0, -1, 3], [4, 18, -2, 8,…

A: We have to decide whether the given vectors are linearly independent. Then, we can proceed further.

Q: Find the coordinate vector of a = [*]B= -10-30- 2 with respect to the basis B = for R³.

A: Given: It is given that, x→=42-4 and B=152, 01-6, 001. To find: We have to find the coordinate…

Q: Find the stable vector of 0 0 1 1 P 2 1 3 3 ..-

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

Q: Find the coordinate vector of = 48 [B = 5 -1 with respect to the basis B = 0 {} for R³.

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Q: c) Consider the vector X₁. -3 = [³3] i. Express x₁ as a linear combination of the standard basis…

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Q: The vectors B= = [x]B= = -{].M]} 8 form a basis. Find a vector x given the B-coordinates of x are

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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.