Let V₁,..., Un be vectors in C, and let A = (ai,j)1

Q: (c) Show that if a span{b₁,b2, ..., b;} then bib{T bi bi (0.0.3) Hint: You can prove the…

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Q: Let v1= 2,5, 3 ) , v2 = ( 1, 1, 1 ) and v3 = (4 , -2 , 0 ) are vectors in R3 then are .a Linear…

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Q: -2x – 4y + 2°z = 1 ) %3D Solve the following linear system. 3x2 + 2x3 – x4 + 2x5 = a 3x1 -9x2 + 7x3…

A: by backward substitution find values

Q: Let A and B be vectors in R. Show that ||A|| = || B|| if and only if A+ B is orthogonal to Ã- B.

A: To solve the given orthogonality problem related to vector.

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

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Q: Are the following vectors linearly independent? Yes No , ,,

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Q: Find all the vectors of the family (2-jx, j4, 2-j5, jx) that are of hermitian length equal to 21.

A: Let Y=2-jx,j4,2-j5,jx Length =Y=4+x2+42+4+25+x2   Y=49+2x2 49+2x2=2149+2x2=2122x2=392x=±14

Q: Find all values of a such that the vectors = and are perpendicular

A: Given:The vectors are  and  are perpendicular.To Find:The value of .Concept Used:When two vectors…

Q: If p = a₁ + a₁x + a₂x² and q = bo + b₁x + b₂x² are any 2 vectors in P². Defined function: f(p, q) ==…

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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: Let j = | and ü .Write j as the sum of two orthogonal vectors, it -2. %3D an {u} and ¤2 orthogonal…

A: Given:- →y=-69  →u=5-2

Q: Find x∈R such that vectors a = and ?=. are equivalent

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

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Q: Suppose v1, ..., vn are linearly independent and Span({v1, .., vn}) = V , then if W ⊂ V and W…

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Q: |Let j and ū = -4 Write j as the sum of two orthogonal vectors, 1 in 9 Span {u} and 72 orthogonal to…

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Q: Use Exercise 47 to show that if cos α, cos β, and cos γ are the direction cosines of a vector v,…

A: cos2α,cos2β and cos2γ are the direction cosines of the vector v

Q: 4.) Are vectors Linearly independent? 2 3

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Q: Let x = (2, 5, 1) and y = (−1, 3, 2) be two vectors in R3. Compute xTy. Compute xyT. Are x and y…

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Q: 4. a) b) Let x = 27 + 3j - k, y = i- j + 4k and Z = −3ỉ + ]. Express the vector x – ỷ – 3ž in terms…

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Q: Are the following vectors linearly independent? , ,

A: A set of vectors v1,v2,...,vk is linearly independent if the vector equation x1v1+x2v2+···+xkvk=0…

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 the is a non-negative integer

A: The number of non-negative integer solution to the vectors…

Q: Q7) True or False, and Justify your answer. If v1, v2, ... V4 are in Rª and v3 = 2v1 + v2, then…

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Q: 2. Consider the collection of vectors --0·00) 2 S = Is S linearly independent or linearly dependent?…

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Q: Let Q "Ax – x'b – C be such that A is positive definite. | Which of the following statements is…

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Q: Let v1= 2, 5 , 3 ), v, = ( 1 , 1, 1 ) and va = (4, -2 , 0 ) are vectors in R3 then are .a Linear…

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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: 2 -7' Let j = and u .Write j as the sum of two orthogonal vectors, , in Span {u} and 2 orthogonal to…

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