7) Three different vectors in R2 that have a norm equal to 5 are:

Q: Given two non-zero vectors a and b such that abs(a+b)=abs(a-b), find the value of a*b (dot product…

A: Given Two non-zero vectors a and b such that  a+b=a-b            ...........1 The dot product of and…

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

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Q: Consider the collection of vectors --000 1 Is Slinearly independent? Carefully explain your answer.

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

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Q: Find each of the following Given: u = ; v = ; w = 1. u.v 2. (u.v)w 3. u.(2v)

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find the best approximation to z by vectors of the form c, v, + C2 V2- 3 3 1 - 5 1 - 2 V2 = 4 - 2 3…

A: To Find the best approximation to z by vectors of the form c1v1+c2v2.

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: cannot be found in such a general cas explain why. In either case, justify you 2) Let a and b be two…

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Q: 21. Use vectors to prove that (a² + b³)(c² + dď²) = (ac + bd)² for any four numbers a, b, c, and d.…

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Q: Given two n x 1 vectors with arbitrary real entries: a = Which of the following computes in MATLAB?…

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Q: how that vectors[ A-2i+ 3j - 2k,B=I +2j+ 4k ] are perpendicular to each o

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Q: make an example and prove it about five vectors spanning R⁴

A: Given: Five vector spanning R4  We need to form an example and prove the given statement 'Five…

Q: a The set S= {(); a # 0} is Select one: a. Is closed under scalar multiplication only b. Is closed…

A: As per guideline we have to solve one question

Q: 2) How many different vectors are drawn here? -/

A: 3 vectors are same which has same direction and magnitude and other 2 vectors are same in direction…

Q: (b1, b2, ..., bn) be any two vectors in R". The inner product Let a = (a1, a2, . .. , an) and b =…

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Q: (b1, b2, ..., bn) be any two vectors in R". The inner product Let a = (a1, a2, ..., an) and b = (dot…

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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: Let a = (a1, a2), b = (b₁,b2) be vectors in R². The area(a, b) is given by 1b₂-a2b₁. (a.) Show that…

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Q: 3) |x| = 7, y = 8, and|x - y = 10, determine | x + y. Hint: sketch out these 4 vectors on the same…

A: We know that the vector parallelogram rules  ||A+B||^2+||A-B||^2=2||A||^2+2||B||^2

Q: why is it not all 4 vectors span W?

A: Lets look at how span of a set is defined :

Q: 4 16 -- 12 -21 4. Is the vector in the span of the vectors 10 12 -8 and 8 ? Explain!

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Q: 5. Determine if the vectors x² + x, 2x²,2x − 3, 9 in P3 are linearly independent or linearly…

A: In this question, we will check the given vectors is linearly independent or dependent.

Q: 1. Let V₁, V2,...,Vn be n vectors in a vector space V. Explain what it means to say that these…

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Q: IH A and B are any two vectors in V, prove that (A- B) x (A + B) = 2(A X B).

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Q: Express each vector in terms of i, j, and k. a) [5, 6, -4] b) [0, –8, 7]

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Q: have 10 vectors in R¹0 which are linearly independent, 1.) If you do they span R¹0? Explain your…

A: We will use the fact that dimension of R^n is n to answer the given question.

Q: Show that if x and y are two vectors, then

A: To show : If x and y are two vectors, then x-y≤x±y≤x+y Pre-requisite :  Cauchy-Schwarz inequality…

Q: 2a)Use triple scalar to verify that the following vectors are not coplanar. a=[-2,1,0], 5=[-3,4,5],…

A: Given problem:- 2a)Use triple scalar to verify that the following vectors are not coplanar.…