5. a) Prove that -2-M u-+ for all vectors in R". b) Explain parts a) geometrically.

Q: Let u and v be non-zero vectors in 3-space. Prove that u and v are perpendicular if and only if |u…

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

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Q: The norm of the vector u = (1, 2, 3, 4) is 30. True O False

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Q: (b) How can you use vectors to determine whether four points in 3-space lie in the same plane? 2.

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Give an example of a set of nonzero vectors in R3 that generates R3 but is not a basis for R3.…

A: Definition 1 : A basis β for a vector space V is a linearly independent subset of V that generates…

Q: Prove that llu - vll >=llull -llvll for all vectors u and v in Rn.

A: According to the given information, it is required to prove the inequality.

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: Which of the following cannot be defined as an inner product between two vectors (x0, Yo) and (¤1,…

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Q: Let y = and u = Write y as the sum of two orthogonal vectors, y, in the span of u, and y, which is…

A: Solution

Q: Show that the vectors are orthogonal.

A: Let the given vectors be v=0i+-4j,u=-7i+0j.

Q: Use vectors to prove that a parallelogram is a rectangle if and only if its diagonals are equal in…

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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: Show that if u and v are n-vectors, then u · v = uT v.

A: Consider the n vectors  u=u1u2u3.un,v=v1v2v3.vn

Q: Prove that for any vectors u, v, w , the set span{u+v,u – v, 3u – 3v + 2w} contains u, v, and w .…

A: A vector v is said to be contained in span of set S  (span(S)) if vector v can be written as a…

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: Construct a geometric figure that illustrates why a line in R2not through the origin is not closed…

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Q: 1. Prove using vectors that the points (-1, 3, 3), (0, 1, 2), (2, 2, 2), and (3, 0, 1) are the…

A: Note: I have solved this above proof by two vector method but is not correct point for…

Q: 19. Show that there are infinitely many vectors in R# with Euclidean norm 1 whose Euclidean inner…

A: To prove:                 There are infinitely many vectors in R with Euclidean norm '1' whose…

Q: nay construct orthogonal vectors a an V such that for each k

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Q: Find an explicit description of Nul A by listing vectors that span the null space.A = -6 4

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Q: a) Prove that ||u + v|| = ||u - v|| if and only if u and v are orthogonal, (b) Draw a diagram…

A: a) Suppose u,v are orthogonal. Now…

Q: Show that if u and v are any vectors in R2, then| |u+v| |2 ≤ (| |u| |+| |v| |)2 and hence | |u+v| |≤…

A: Let the component of u and v are ; u=(u1, u2)T v=(v1, v2)T Then; This gives us the inequality;…

Q: 7. For the vector ū = (1,2,3), compute the 1-norm, the 2-norm, and the 0-norm.

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Q: Prove that A•(AxB) =0. Note that A and B are vectors.

A: Prove that A•(AxB) =0. Note that A and B are vectors

Q: 50 Express the vector b = – 11 as a linear combination of the %3D – 48 - - 14 5 - 10 - | - vectors…

A: the question are based on the concept of linear combinations. we will form the system of linear…

Q: Let O be any point in space. a, b, c are the vectors from O to the three vertices of parallelogram…

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Q: five vectors in Span v1, V2}. Do not make a sketch. 8 - -

A: In this question, the concept of the span of the vector is applied. Span The smallest linear…

Q: 18. Find the vector u in 2-space of length 2 that makes an angle 0 4.

A: A vector having length u→ and makes an angle θ is given by  u→ = u→cosθ i^ + u→sinθ j^

Q: 19. Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1, –4,0), v = (-1,–1,2,2),…

A: Step:- 1 Given that u=2, 1, -4, 0,  v=-1, -1, 2, 2,  w=3, 2, 5, 4 Now, first we check the given…

Q: Let p and q be two non-zero vectors. By using the definition of vector product show that pxq =…

A: In the given question, calculate the area of the parallelogram where two sides p and q are given.…

Q: Which of the given sets of vectors in R3, with the standard inner product, are orthogonal,…

A: a) Given, 01-1,011,200 Consider the vectors, u=0,1,-1v=0,1,1w=2,0,0 Now find the inner product of…

Q: 27 (3) (Projections) Compute the projection of -2 onto the plane spanned by the vectors 2 and

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Q: 7) Find all vectors v in F such that 2v + ) -)

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Q: 15. Let v = and u = be two vectors in R2. %3D a) Use the formula projyu = V to compute the…

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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: In Exercises 3–6, find an explicit description of Nul A, by listing vectors that span the null…

A: The matrix is A=13-4-3101-31000000

Q: Suppose that u and v are vectors in 3-space such that |u||= 5 and u · v = 7.

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Q: 2- Show whether the set of vectors S={ ,,} is a basis of R3 ?

A: Given the set of vectorsS={<3,2,2>,<−1,2,1>,<0,1,0>}

Q: Find the signed volume of the slanted box in R“ generated by the vectors 27 11 11 -2 3 , U2 = V3 =…

A: Form a matrix of the given vectors, A=v1v2v3v4=0-2-1-12-1-236-10-23030 The volume of the slanted box…

Q: 1. Compute the angle Pair Of vectors in Standard inner producy on Mzz. between tre following Mzz…

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Q: Show that the vectors (1,1,0), (1,0,1), and (0,1,1) generate F3.

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

A: In the given question we have to find three different vectors in ℝ2 that have norm equal to 5.

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

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Q: 3- Rewrite the vector v in the form a + ib, where vectors a and b have only real components.

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Q: Find the unit vectoru in the di rection of the vectorv=3(2, 2, 1).

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Q: Find a so that the vectors v = i- aj and w = 7i + 7j are orthogonal. ..... une on integer or o…

A: If two vector orthogonal then dot products will be zero

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.