_3. Let x be a convex combination of {y1, . . , yk }. Assume in turn that each y; is a convex combination of { yi,1, the vectors { yi, j }. ... Yi,k; }. Prove that x is a convex combination of .. ,

Q: ii) Show that any four vectors oj, , 5, Vi in R are linearly independent.

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Q: 1. Let v = PQ where P = (3,4,0) and Q = (2, 3, 1) Find a vector u that is parallel to V but with a…

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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: 2. Show that if the vectors v,, v2, .,Vm are mutually orthogonal then they are linearly ...…

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Q: The set of which vectors is a basis for A+B Hint: A+B= [aí az a b b2 ba

A: Given A=spana1→, a2→,a3→ , B=spanb1→, b2→,b3→ where, a1→=1,2,0,-1 a2→=0,2,-1,1 a3→=3,4,1,-4…

Q: Let V = {u, v, w} where u = (5, -1, 1), v = (3,5,-5). Find that would make a DEPENDENT set of…

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Q: Let W be the set of all vectors of the form ū = H V = [-5s- 2t] 5s + 3t 5s + t . Find vectors ū and…

A: Let S={u,v} be a linear independent set and generate W . Then W=span{u,v} .

Q: 2. Let p₁ = (2,-1,8), p2 = =(5, -3,9) and p3 = (0, -1, 14) (a) Show that the three points define a…

A: Note: Since we only answer up to 3 sub-parts, we'll answer the first 3. Please resubmit the question…

Q: 13. Write the reduced echelon form of a 3 x 3 matrix A such that the first two columns of A are…

A: 13. Given that A3-21=000. We have to find a 3×3 matrix Athat has first two columns of A are pivot…

Q: Consider the vectors u=(2,3,-5), V = (-3, -2,6) and w=(-4,8,4). Calculate u.v

A: We have to find u.v

Q: Suppose that x = (2,1,0,3),y=(3,-1,5,2), and z=(-1,0,2,1). Which of the following vectors are in…

A: A vector v is said to be in the span of the vectors v1, v2, v3, ……, vn if the vector v can be…

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: "ove that if two vectors are linearl y de pendent, e of them is a scal ar mul it ple of the other.

A: Two vectors are linearly dependent, one of them is a scalar mulitple of the other.

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: Two linearly independent vectors in R3 span R2, is that true

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Q: Let u4 be a vector that is not a linear combination of {u₁, U₂, U3, }. Select the best statement. ©…

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Q: Which of the following sets DA. B. -1 THE DC. vectors are linearly independent? TELBEL [BLETE] D. 8…

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

A: Given u and v be two vectors in ℝ7 satisfying u×u=4, w×w=16, u×w=8

Q: Show that if u and v are vectors in the three-space, then ||u x v||? = ||u|| ||||² – (u · v)²

A: u and v are vectors.

Q: Determine whether or not the following set of vectors span R³, (i) {(1, 1, 2), (1, -1, 2), (1, 0,…

A: Span of R3 .

Q: Which of the following is a necessary condition for a set of vectors {V1, V2, ..., Vp} in R" to be…

A: Given that the set of vectors v1, v2,...,vp in ℝn. We have to find the necessary condition for the…

Q: Q3 O Let w-l(a,b,c), b= 3a} is Sub Sehoof RE a Sub Spaceef R32 is s w X, = i +2j - K , Xz= -3i+2j-R…

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Q: Q1. Consider the following vectors: -- () ---- () --C) 2 3 1 3 (a) Do the vectors i, u, w span R³?…

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Q: S= {(1,1,1), (1,2,-3), (5,-4,-1)} is a set in R'. Show that a) Sis orthogonal. b) Write w = (1, 5,…

A: Orthogonal set is the set in which dot product of two vectors is zero.

Q: Suppose V1, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(v1, V2, V3) such…

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Q: 12 If a, x and y are three are given by b=x-(x along a and b respecti

A: We know that three vectors are mutually when A.B=0,B.C=0,A.C= 0 Means A is perpendicular to B when…

Q: Suppose that u is a unit vector which is orthogonal to some other vector . Then u (u + v) + ||projzu…

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Q: 5. [7.6] If vectors ū=(5,2,-1) and = (2,-1, 3) then... a) determine u x v. b) Explain the geometric…

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