Let ?1 = (4 3 2 1), ?2 = (−2 0 -1 0), ?3 = (0 3 0 1) a) Find the subspace of R^4 spanned by these vectors. b) Are the vectors linearly independent? c) Determine a basis for R^4 that contains as many of the above three vectors as possible.

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A: Linearly dependent vectors

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A: Explanation of the answer is as follows

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

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A: Full and detailed solution is given below. Dim(w) is number of elements in basis(w)

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

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Q: The vectors (attached) form a basis of R^3 (R = Real numbers) if and only if k does not equal blank

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Q: Find a basis of the subspace of R* consisting of all vectors of the form X1 -8x1 + x2 —6х — 2х2 -6x1…

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Q: Determine the following three vectors {, , } forms a basis for R^3. Expalain your answer.

A: Answer  Given  <2,1,0> , <4,2,2> and <-2,-1,3>  Let check whether they are…

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.