Suppose {u1,u2,...,un} is a set of vectors that span V, and that {v1,v2,...,vk} is an independent set of vectors in V. Explain why v1=x1u1+x2u2+...+xnun must have a nontrivial solution. Explain why we may assume x1≠0. (Hint: x1 is the first unknown because u1 was the first vector in our spanning set.) Explain why this means u1 is in the span of {v1,u2,...,un} Explain why this means {v1,u2,...,un} also spans V.

Q: 1] Suppose that W, N are non-zero two- dimensional vectors which are not parallel. Show that if C is…

A: Please rate and feel free to ask any query about any part of the question

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A: To find a vector v satisfying 3v+(5,20)=(11,17).

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Q: 2 3. Show that that the vector u = -5 is a linear combination of the vectors v1 3 2 ------ 2 U2 = -4…

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Q: Find Projwv and Decompose v into two vectors v1 and v2​, where v1 is parallel to w and v2 is…

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A: Solution is given below:

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Q: Two vectors ñ and m are said to be orthogonal if ñxm3D0

A: Thanks for the question :)And your upvote will be really appreciable ;)

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Q: 2b.) Suppose u, w are two vectors in R' satısfyıng uXu = 4, wXw uxw = 8. What is the distance…

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Q: linear algebra

A: To prove the linear independence of the three given vectors.

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A: Answer

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Q: Determine whether the set of vectors in P2 is linearly independent or linearly dependent. S = {2 +…

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Q: given the vectors from R3 v, = (2 0 3), v2= ( -1 3 0), v3=(2 4 –1) %3D (-5 0 3) belongs to span{v,,…

A: Given vectors are v1→=2,0,3, v2→=-1,3,0, v3→=2,4,-1. To determine: u→=-5,0,3 belongs to span v1→,…

Q: 1] Suppose that W, N are non-zero two- dimensional vectors which are not parallel. Show that if C is…

A: We have to solve given problem:

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Q: 17 jp 17 Jlgull>> حفظ الإجابت 3 درجات Two vectors ñ and m are said to be parallel if ñ m-0

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Q: 3. Show that that the vector u = |-5 is a linear combination of the vectors vị = |-3 3 2 V2 = -4 and…

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Q: Determine whether the set of vectors in P2 is linearly independent or linearly dependent. S = {2 +…

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A: This is a problem of vector calculus.

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.