ind a basis for the set of vectors in R' of the form а + 5с + d 2а + 5b — 8с A = —а — 4b + 7d - b+c+3d vhere a, b, c,and d are real numbers.

Q: 2- We can write the vector x = (19,–1,–) in R³ as a linear %3D combination of the vectors x1 = (4,2,…

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Q: There exists a set of three nonzero orthogonal vectors in R. Select one: O a. True Ob none o hese…

A: Set of orthogonal vector of R^n contain at most n vector .

Q: (b) The general fact that fcu++eUn]e== c\]j + .. + ca[vn]s allows for rewriting the equation above…

A: It is an important part of statistics. It is widely used.

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: 5. Show that the vectors a = 3i- j+4k, b = i- 3j – 2k and c = 4i – 3j+2k are linearly independent.…

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Q: Show that the vectors V1 = ( 1, 1, 2, 4 ), V2 = ( 2, -1, -5, 2 ), V3 = ( 1, -1, -4, 0 ) and V4 = (…

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Q: Г10] Let ÿ = 7 and i = -2. Write y as the sum of two orthogonal vectors, j1 parallel to u and j,…

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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: 7. Compute Let a, b, and c be three vectors in the plane 3x – 5y + 6z -4b — 7c) (-3і + 5j — 6k).

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Q: -91 Let y = -3 and u = and 2 orthogonal to u. x₁ = 4 -2 Write y as the sum of two orthogonal…

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

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Q: Express the vector (4, 7, -2) as a combination of the standard basis vectors i = (1, 0, 0), 3 = (0,…

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Q: 1. Determine whether the vectors vi (1,2,3), v2 (2,4, 5), and v3 (1,0,0) are independent.

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Q: Show that the vectors 1 – t,1+ 2t² , t² +t+1, t² + 2tare linearly dependent and indicate how one of…

A: Given Vectors:V1 = 1-tV2 = 1+2t2V3 = t2+t+1V4 = t2+2tgiven vectors are linearly dependent, then…

Q: 1. Let b1, b2 and z be vectors in R" such that bị and z are orthogonal and b2 and z are also…

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Q: Consider vectors a = (2, -8), b = (-1, 4), andc = 0. Determine the non-zero scalars a and B such…

A: Consider vectors a=(2,-8) , b=(-1,4) and c=0. We have to determine the non-zero scalars alpha and…

Q: Determine whether the given vectors (1, 1,-1, 1), (1,-1, 2,-1), (3, 1, 0, 1) in R* are lincarly…

A: Given vectors are: (1, 1, -1, 1) , (1, -1, 2, -1) , (3, 1, 0, 1) We have to determine whether the…

Q: 1. Consider the vectors (2, 1,0, 2], [3, 1, 0, 1], [1, 1,0, -1] in R'. Decide whether they…

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Q: Consider the vectors in R2 3 2 (3) Express as a linear combination of the vectors Select one:…

A: Here we have to find the linear combination.

Q: The vectors v.= span R but do not form a basis. Find two different ways to express -3 - 3 as a…

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Q: a) Determine k so that the vectors (1,–1, k – 1),(2, k, –4) and (0,2 + k, -8) in R³ are linearly…

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

Q: . Show that the vectors a = 3i-j+4k, b = i-3j-2k and e = 4i-3j+2k are linearly independent. Find…

A: Note:- We are entitled to solve only the first question, unless specified. Given vectors: a=3i-j+4k,…

Q: Suppose that ā and b are nonzero vectors. Under what circumstances is comp;b = comp;a? Under what…

A: A vector has 2 components, magnitude and direction which is represented by cos and sin angles. A…

Q: 1. Consider the vectors [2, 1,0, 2), [3, 1, 0, 1), [1, 1,0, -1) in R. Decide whether they…

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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: 2 Consider A = -2 null(A). 4 2 2 4 -4 -2 -2 -4 -2 0 1 Give a set of vectors that spans each of im(A)…

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Q: 3. Find two unit vectors that are orthogonal to both j +2k and į -2j + 3k.

A: Solution is here

Q: Find non-zero vectors I and 7 that are both orthogonal to and orthogonal to each other.

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Q: prove that 12 div A; = √√√x² {√8 8¹k Ax} = dxr div A¹, where A; and Ai are the covariant and…

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Q: Prove that a(-3,2) and b (2,-3) form basis vectors in xy plane

A: a set is said to be basis if set is linearly independent and it spans the space.

Q: Determine whether the vectors v1=[12 1]^T , v2=[1 O 2]^T and v3=[5 6 7]^T are orthogonal vectors Non…

A: We have to check weather the given vector are dependent or not.

Q: 5b- За Let W be the set of all vectors of the form Find vectors i and v in R such that W = span {i,…

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Q: Determine k so that the vectors (1,–1, k - 1), (2, k,-4) and (0, 2 +k,-8) in R linearly independent.…

A: The detailed answer and explanation is given below:-

Q: In R3, let S be the set of vectors 3 S = {V1, V2, V3, V4} = -3 -2 -4 -4 a. Explain why S spans R³…

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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: 4) Find all vectors vE C? such that (1 + i)v + () = () 3+ 6i

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Q: Find a so that the vectors v = i- aj and w = - 9i - 8j are orthogonal. (Type an integer or a…

A: As we know that; If two vectors v & w are orthogonal to each other then the dot product or…

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

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Q: 5. Show that the vectors a = 3i-j+ 4k, b =i-3j–2k and e = 4i– 3j+2k are linearly independent. Find…

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Q: Find a basis for the set of vectors in R^3 in the plane 3x - 2y + z = 0. Also state the dimension.

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Q: The set of vectors -15 is a basis for R2. Select one: O True O False

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Q: 4. Determine whether the vectors a = 2i – 3j+ 5k, b = 3i+j – 2k and c =i- 7j +12k linearly dependent…

A: To check whether the vectors are linearly dependent or linearly independent.

Q: 2 3. (a) Find two vectors of norm 1 that are orthogonal to the vectors u = -3 and v = .3 4

A: What is the inner product of the vector space of 2 by 2 matrices. We assume it is Frobbenius inner…

Q: and v2 = -3 3. be two -8- Question ( Let vi %3D vectors in R. Show that v belongs to span {v1, v2 }.

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Q: Find a so that the vectors v=i- aj and w = 7i- 10j are orthogonal. (Type an integer or a simplified…

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Q: 1. Determine the single positive vector that is the resultant of: CD ED + AB - CB D

A: Vector AB = - Vector BA

Q: There are 6 linearly independent vectors in R°. O True False

A: We know that the dimension of the vector space R5 is 5.

Q: Write x as the sum of two vectors, one in Span {u,,u,,u3) and one in Span (uA. Assume that (u,,.u}…

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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.…