Which of the following set of vectors form a basis for R^2 space? 2 points O (0, 5), (0, 3)} O (1, 0), (2, 0)} O {(1, 4), (3, 12)} O {(5, 2), (6, 0)}

Q: Let u1 = (-1,1,3), u2 = (2, 1, –3), uz = (3,0, 1) are three vectors. %3D Find expansion of the…

A: We have to write in linear combination form

Q: 2. Determine whether the vectors v, are orthonormal. If not, normalize them to produce an…

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Q: Determine a vector that is orthogonal to both (1, 4, −1) and (5, 1, 0).

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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, -2, -2), (2, 3, 4) is < 2, – 10, 6…

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Q: 1. Find the set of vectors orthogonal to 2 by using the theory of Null spaces. Describe this set…

A: According to our guidelines we can solve only first question  and rest can be reposted.Thank you

Q: Consider the vector v between (-5,5, –3) and (1,1, 1).

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Q: What is the scalar projection of á = (1,0, 1) onto b = (0, 3, 4)?

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Q: Give two examples of infinite dimension vector spaces.

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Q: (a) Show that the vectors ui = (3, 1,0), u2 = (-1,3,0) and uz = (0,0,4) form an orthogonal basis for…

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Q: Explain the term A Basis for a Vector Space.

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Q: Determine whether the set of vectors is orthonormal. If the set is only orthogonal, normalize the…

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Q: . Determine if the vectors (3,2,0) , (-3,0,1) , and (1,1,–9) span all of R’ . Do these vectors form…

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Q: Recail that two nx matrices A and B are Similer if there is an invertible matrie P Such thet p' Ap…

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Q: . Show that the vectors = (0, 3, 1, -1); v, =(6, 0, 5, 1); v, = (4, -7, 1, 3) form a linearly…

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Q: Express the vector (-1,5, –6) in R³as a linear combination of (2,0,7), (2,4,5) and (2, –12,13).

A: Solved below

Q: Find the vector projection of (3, 3, 4) onto (–1, -2, 2).

A: Projection of u onto v is given by.

Q: Find a vector in 3d space whose magnitude is 4 and whose components have the largest possible sum

A: Find a vector in 3D space whose magnitude is 4 and whose components have the largest possible sum.…

Q: Find an orthogonal projection of (6, 0, 0) (1) along the vector (1, 2, 1) (2) On the plane…

A: (1) Let a→=6,0,0, b→=1,2,1 Then orthogonal projection of a→ along the vector b→ is a→·b→b→·b→b→…

Q: Find the coordinate vector of (-1, 32) relative to the basis {(1, 3), (-1, 4)}.

A: We use the definition of coordinate vector relative to a given basis to answer the given question.

Q: (1 point) Find a vector orthogonal to both (-1,5,0) and to (0,5, 5) of the form (1,

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Q: Consider the vector v between (-5, 5, –3) and (1, 1, 1).

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Q: Compute the Binary distance between vectors [2, 1, 0] and [8, 5, 0].

A: Given vector points are (2, 1, 0) and (8, 5, 0)  Let (x1 , y1 , z1 ) = (2, 1, 0) And (x2 , y2 , z2 )…

Q: Find a basis for the vector space of all 3 × 3 symmetric matrices. What is the dimension of this…

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Q: Decide whether the vectors [2, 9, -1, 4, 7, 8, 10, 9], [11, 2, 5, -9, 0, 0, -1, 3], [4, 18, -2, 8,…

A: We have to decide whether the given vectors are linearly independent. Then, we can proceed further.

Q: Decide whether the vectors [2,9,-1, 4, 7, 8, 10, 9], [11, 2, 5, -9, 0, 0, -1, 3], [4, 18, -2, 8, 14,…

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Q: 2. A 2D-subspace (manifold) in 3D- space is defined by the two vectors d;=é,+ê,-2êzand ā,=ê,+2êz-3ê,…

A: A 2D-subspace (manifold) in 3D - space is defined by the two vectors a→1=e^1+e^2-2e^3 and…

Q: how can one check that a set with two operations, addition and scalar multiplication, is a vector…

A: One can check for a set to be a vector space by checking all the above axioms. If a set V with two…

Q: Find an orthonormal basis for the subspace spanned by (0,1,2), (-1,0,1) and (-1,1,3).

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Q: Obtain a set of orthonormal vectors by Schmidt method: u = (1, 1,0,1), uz = (2,0,0, 1), uz (0, 2,3,…

A: According to gram Schmidt method  orthogonal vectors can be obtained as: x1=u1x2=u2-&lt;u2,…

Q: Determine whether the given orthogo­nal set of vectors is orthonormal. If it is not, normalize the…

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Q: Give two examples of finite dimension vector spaces.

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

A: Dear students you have asked multiple questions. As per our policy your first question will be…

Q: Represent the vector ⟨16,8,−14⟩ in terms of the ordered basis B={⟨5,−2,−2⟩,⟨1,−4,2⟩,⟨−1,−5,3⟩}.

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Q: (7,4) by 210 4. Use matrices to rotate the vector degrees counterclockwise about the origin.

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Q: Define whether these vectors are linearly independent! --- u =| 2 3, 12.

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Q: Make the vectors u1=(2,0,-1,1), u2=(1,1,-1,3), u3= (-1,1,1,-1) orthonormal.

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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, 0, -2), (2, 3, 4) is

A: We will solve the problem

Q: Find a vector orthogonal to both (-4,-4,0) and to (0,-4,-4) of the form (100)

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Q: Given the basisof R° consisting of the three vectors n = (-1,0,0) , ½ = (0,1,0) and V3 = (0,-1,1) .…

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Q: Find a subset of the vectors v1=(1,−2,1,−1), v2=(0,1,2,−1), v3=(0,1,2,−1) and v4=(0,−1,−2,1)that…

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Q: Determine whether the given orthogo­nal set of vectors is orthonormal. If it is not, normalize the…

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Q: Find a subset of vectors v1 = (1,0,1,1), v2 = (-3,3,7,1), v3 = (-1,3,9,3) and v4 = (-5,3,5, –1) that…

A: To find subset of vectors that forms a basis for the space spanned by the vectors. Form a matrix:…

Q: Find a vector orthogonal to both (-4,5, 0) and to (0, 5, 4) of the form (1,

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Q: 6. Compute the projections of [1, – 1,0, 1] on the vector [0, 1,0, 2]. |

A: Let v = [1, -1, 0, 1] and u = [0, 1, 0, 2]

Q: Find an orthonormal basis spanned by a set of vectors V1 = (2, 2, 1), V2 = (−2, 1, 2), V3 = (9, 0,…

A: We will first find orthogonal basis using Gram-Schmidt Process, then orthonormal basis

Q: Express (-1,2,4) as linear combination of x = (-1,2,0), y = (0,-1,1) and z = (3,-4,2) in the vector…

A: A vector is a quantity that has both magnitude and direction. It can be also defined as the…

Q: The normal vector of 2x + 3y - z + 5 = 0 is: O [3, -1, 5] O [2, 3, -1] [2, 3, -1, 5] O (-2, -3, 1]

A: Answer :  From question given that the Normal vector form is  ; 2x + 3y - z + 5 = 0

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.