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: 8. If {V1, V2,..., ,}is a linearly dependent set of vectors, prove that one of these vectors is a…

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Q: One of the following vectors lies in span{ 2+x + x?, 3+x- 2x2} (A) 4+ x – 7r² (B) 4+ x – 4x? (C) 4 +…

A: Solve the following

Q: 10 -00-0 7 12 5 -8- Are the vectors 6 and linearly independent? Explain! 8

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Q: If possible, write the vector w as a linear combination of the vectors V₁, V2, ..., Vk. If it is not…

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Q: 9 One requirement can be met while the other fails. Show this by finding (a) A set of vectors in R²…

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Q: 2.) Wrile pach vector below of the vectors in s.Cif possible), 0s a linear combination 5=d…

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Q: A make linearly dependent set of vectors in R^4 Plase make sure you list three different reason why…

A: There are three different reasons why the set of vectors in R^4 is linearly dependent. If a set…

Q: Given three non-zero vectors, a, b & C, is it possible to evaluate a b Explain with an example. •6•²

A: We have given three non-zero vector.

Q: Three unique non-zero vectors a, b, and C are defined by four points in space. Select all of the…

A: Proceed as shown below

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Q: 5. Determine which sets of vectors are orthogonal. (a) 1 ↑ 1 0 -5 2 1 5 -309 (b) -4 2

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Q: 7. Let -3 6 -0--0-0-H [-] 8, V3 11 a. How many vectors are in {V₁, V2, V3}? b. How many vectors are…

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Q: Let -3 ----------- V3 2 V1 = 6 a. How many vectors are in {V₁, V2, V3}? b. How many vectors are in…

A: Let and

Q: What if the vector v was [ 7, 11, 3]

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Q: ー0 Let A = -3 -8 %3D そ 14 Label the colmn vectors C ,s,C3, and Cy respeutively. let b. be a linear…

A: The given matrix is ;                     A =  577-10-311-86713914 If  C1 , C2 , C3  and  C4  are…

Q: Let Is w a linear combination of the vectors V₁, V₂ and 3? choose 13 -14 -4 --[H], -- [5] -- [13] D…

A: Given that the vectors w=-146 , v1=5-4 ,  v2=-4-3 ,  v3=11 .

Q: (In set notation: (| x ER).) In the following, determine whether the statements are True or False,…

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Q: 6. Determine if the vectors à = [−1, 5, 3], b = [−2, 4, 7], and ₹ = [10,7,1] ar are coplanar.

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Q: Let {u₁, 12, 13} be a linearly independent set of vectors. Select the best statement. {u₁, U2, U3,…

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Q: 1) Determine if the vector b can be written as a linear combination of the vectors a₁, az, and al 1…

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Q: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

A: we will write the given vector as linear combination of vectors in as and find the unknown…

Q: If u • vx w or v • or w • v equal to zero, then the vectors u, v , and w are coplanar... True False

A: Concept Used: Three vectors are said to coplanar if their scalar triple product is zero That is  [u→…

Q: d) the transpose of x. 2- If x= [2 8 5; 9 7 1], b=[2 4 5] find: a) find the maximum and minimum of…

A: Given:x=285971 and b=245To find:a) The maximum and minimum of x.b) add the vector b as a third row…

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.