Let v1=[-2,2,1], v2=[-8,7,4], v3=[-29,25,14], w=[6,6,1] is W in {v1,v2,v3}? how many vectors are in {v1,v2,v3}? How many vectors are in span {v1,v2,v3}? is w in the subspace spanned by {v1,v2,v3}?

Q: 5. Show that if each of the vectors {Bo, B1,...,B,} is a linear combination of {a1,a2,...,a,}, then…

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Q: Determine whether the vectors u = 2 – x + 3x?, v = 4 +x + 2x?, and w = 8 - x + 8x² span P2 (the set…

A: The set {p1,p2,p3} will span p2 if and only if they are independent  so, here we test if the vectors…

Q: 4. Find the largest possible number of independent vectors among V1 =, v2 = , v3 = , v4 =, v5 =, v6…

A: We have the vectors: v1=1,-1,0,0v2=1,0,-1,0v3=1,0,0,-1v4=10,1,-1,0v5=10,1,0,-1v6=0,0,1,-1 We need to…

Q: 5. Determine the number of vectors (x1,...,x„), such that each x; is either 0 or 1 and i=1

A: (x1,x2,...,xn) is a vector with xi is either 1 or 0.  Now, ∑i=1nxi ≥ k implies at least k of the…

Q: Let u1 = (-1,1,3), u2 = (2, 1, –3), uz = (3,0, 1) are three vectors. %3D Find expansion of the…

A: We have to write in linear combination form

Q: 7. "Let &, n, ở be real numbers and consider vectors (1,5,8²); (1,n,n²); (1,0,0²). Determine the…

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Q: Let w= (-1,4,15), v = (1, 2, 8), v = (3, 0,1). Does w belong to span(v,,v,)? If yes, then write the…

A: We will find out the required solution.

Q: Find all vectors in R' that are perpendicular to both [1,0, 1, 0] and [1,2,0, 1] and then find a…

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Q: Write the vector w = (1, 1, 1) as a linear combination of vectors in the set S. V2 V3 S = {(1, 2,…

A: See the attachment.

Q: Show that v, = (1,0,–1) , v, = (1,0,1) , v3 = (1,1,1) span R’. %3D Express vector v= (4,2, 2) as…

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

Q: . Show that the vectors = (0, 3, 1, -1); v, =(6, 0, 5, 1); v, = (4, -7, 1, 3) form a linearly…

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Q: Find a subset of the vectors that forms a basis for the space spanned by the vectors; then express…

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Q: 3. Show that the vectors v₁ = (0, 3, 1, -1); v₂ (6, 0, 5, 1); v =(4, -7, 1, 3) form a linearly…

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Q: Show that the set is linearty dependent by finding a nontrivial inear combination of vectors in the…

A: we have to show that the set is linearly dependent by finding a nontrivial linear combination of…

Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

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Q: Are the vectors (-3,0,4), (5,-1,2), and (1,1,3) linearly independent in R3?

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Q: Show that if R" = Span(v1, v2, · .· Vk) for some vectors v; of R" with k > n then one can find n…

A: Given:           If            ℝn = Span(v1,v2,..........vk) for vi of ℝn  with k>n, Prove:…

Q: 8. Consider the vectors [11, 2, 0, 1, 0, 2], [0, 1, 1, 2, 1, 2], [2, 1, 2, 1, 1, 1]); [0, 1, 1, 1,…

A: Remark: If no column (row) of a matrix can be written as linear combination of other columns (rows)…

Q: Let a = (7, 10, 1) and b = (10, 3, 6) be vectors. Compute the cross product %3D ахЬ.

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Q: Find all vectors u such that ux(1,1,1)=(8,-5,-3).

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Q: 6) a) Express the vector (8,0,5) as linear combinations of u (1,2,3), v = (2,-1,1), and w (0,1,4)

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Q: 3. Show that the vectors v = (0, 3, 1, -1); v, = (6, 0, 5, 1); v3 = (4, -7, 1, 3) form a linearly…

A: Given vectors are: v1=(0,3,1,-1), v2=(6,0,5,1), v3=(4,-7,1,3)

Q: . Show that the vectors V1=(0, 3, 1, -1); V2=(6, 0, 5, 1); V3=(4, -7, 1, 3) form a linearly…

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Q: Suppose v1, V2, V3 is an orthogonal set of vectors in R. Let w be a vector in span(v1, v2, V3) such…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: When V is spanned by {v1, v2, . . . , vk} and one of these vectors can be written as a linear…

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Q: Let ů,v,,v2,,v, be nonzero real valued vectors in R', such that ū is orthogonal to each v. Show that…

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Q: how that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

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Q: Find a maximal set of linearly independent vectors out of the set {v1 = (1,2, 3, 4), v2 = (2, 3, 4,…

A: From given set of vectors we have to find maximal set of linearly independent factors. Concept: Let…

Q: If {v1, V2, V3} is an orthogonal set of nonzero vectors in an inner product space V, then prov that…

A: This question is related to linear algebra (inner product space).

Q: If there is v1 = (1,3,3), v2 = (0,1,4), v3 = (5,6,3) and v4 = (7,2, -1) is the set of linear…

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Q: How many Linearly Independent vectors in the set {(1, 1, 1, 2), (1, -1, 2, 3), (3, 1, 4, 7), (2, 2,…

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Q: b) Express the vector (–1,5, -6) in R³ as a linear combination of (2,0, 7), (2,4, 5) and(2, –12,13).

A: See the detailed solution below.

Q: Show that the vectors v, = (0, 3, 1, -1); v, =(6, 0, 5, 1); v; = (4, -7, 1, 3) form a linearly…

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Q: 4 2. Decide whether the vectors (1, 2,0,-1], [2, 6, -3, -3], [3, 10, -6,-5] are linearly…

A: Given vectors are ,  [ 1,2,0,-1 ] ,  [ 2,6,-3,-3 ] ,  [ 3 ,10 ,-6 ,-5 ]  (.)  The given vectors are…

Q: Suppose V={v1,v2,...,vn} is a set of nonzero vectors, and let                    x= a1v1 + a2v2…

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Q: Define whether these vectors are linearly independent! --- u =| 2 3, 12.

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Q: Determine whether the set of vectors Q={(-1,1,1).(-1,0,2).(1,2,3)} spans R'.

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Q: 2- We can write the vector x = (19,–1, -) in R³ as a linear combination of the vectors x1 =…

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Q: There are four vectors (1,a,b,c), (1,1,1,1), (1,2,3,1), (3,4,5,3). If the vector space (subspace)…

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Q: How many of the vectors (n-tuples) (1 2 2 -1 ), (-4 0 0 -4), (-1 1 -2 -2 ), (-2 0 0 -2 ), (-3 -2 -2…

A: If for given vectors the zero vector can only be obtained by their trivial linear combination then…

Q: When the set of vectors {u1, u2, . . . , un} is linearly independent and the set {u1, u2, . . . ,…

A: We have given; The set of vectors {u1, u2, . . . , un} is linearly independent and the set {u1, u2,…

Q: Suppose {v1, v2, ..., vp} is an orthogoal set of vectors. Show that {c1v1, c2v2, ..., cpvp} will…

A: Since {v1, v2, ..., vp} is an orthogoal set of vectors, dot products between any two of them will be…

Q: Suppose that v1=(2,1,0,3), v2=(3, 1,5,2), v3 = (-1,0,2,1) ar column vectors temporarily lying down…

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Q: 2. If a set of vectors contains at least 2 vectors that are scalar multiples of each other, then the…

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Q: Find a vector of norm 1 that is orthogonal to the three vectors u = (2,1,-4,0), =(-1,-1,2,2),…

A: The solution is given as

Q: 9. Is the set of vectors {(-2, 2, 0), (1, 1, 1), (8, -4, 2)} over R linearly dependent or…

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Q: Find a vector b such that compab = 2. If a = ⟨3,0,−1⟩

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Q: Express (-1,2,4) as linear combination of x = (-1,2,0), y = (0,-1,1) and z = (3,-4,2) in the vector…

A: A vector is a quantity that has both magnitude and direction. It can be also defined as the…

Q: The normal vector of 2x + 3y - z + 5 = 0 is: O [3, -1, 5] O [2, 3, -1] [2, 3, -1, 5] O (-2, -3, 1]

A: Answer :  From question given that the Normal vector form is  ; 2x + 3y - z + 5 = 0

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.