What is the different between linear dependent and linear independent vectors? Given any three examples

Q: b) Give an example of 5 linearly independent vectors in R*, or explain why it is impossible to do…

A:

Q: 6. If u,v, and w are three vectors in R', describe their linear span.

A: 6. If u,v and w are three vectors in R7, we have to describe linear span.

Q: Show that the vectors below are independent. 1 3 3 3 5 3

A: The given vectors are 123,  -1-15   and  333. Compute the determinant of matrix formed by these…

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

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Q: n span{u} = span{u,v}? If so, when? nat does it mean for a set of vectors to be linearly independent…

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Q: Are the following vectors linearly independent? ,,

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Q: Determine whether the set of vectors is linearly independent: {(1,0,1), (3,4,-3), (2,2,-1)}.

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Q: ,,,

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Q: In each case, find the linear combination of the first two vectors that is as close as possible to…

A: Both part of the question can be converted into the question based on least squares solution of a…

Q: (a) Are the vectors (1,3, 2), (2, 1,3) and (3, 2, 1) linearly independent? (b) Are the vectors (1,…

A: We have to check

Q: Find the length of the vector x=x= |x|=|x|=

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Q: 3 -1 V3= 4 3 4 -2 2. 2.

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Q: Are the vectors (-3,0,4), (5,-1,2), and (1,1,3) linearly independent in R3?

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Q: Determine if the sets of vectors in Exercise are linearly independent. If for any of these, the…

A: Given :           The vectors are 111 , 123 , 1-12   To determine the vectors are linearly…

Q: What is the effect of scaling a Vector? Give an example?

A: we need to explain the scaling of vector. and we  need to give an example. First let us define what…

Q: Are the Following Vectors Linearly Dependent or Independent? 1) (3,4), (4,3) Ans. Indep

A: We have to check the vectors are linearly independent or dependent (3, 4) , (4, 3)

Q: Determine if the sets of vectors in Exercise are linearly independent. If for any of these, the…

A: The set S = {v1, v2, v3, v4} of vectors in R4 is linearly independent if the only solution of c1v1 +…

Q: Are the following sets of vectors linearly independent? Show the details of your work. 17. [3 4 0…

A: We have   Solve using row-echelon form

Q: 2 aj = a2 = az = b = Determine if vector b is a linear combination of vectors a1, a2, and аз. Show…

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Q: Find the length of the vector.v = (5, −3, −4)

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Q: 9. Explain why four vectors is R³ are always linearly dependent.

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Q: We define a median vector of a triangle to be the vector from a vertex of the triangle to the…

A: Let ,The triangle be ∆ABC A(x1, y1, z1)B(x2, y2, z2)C(x3, y3, z3)AM→ , BM→ , CM→ be the medians

Q: A subset of linearly dependent vectors is linearly dependent. Select one: OTrue O False

A: A subset of linearly dependents vectors is not always linearly dependent. Take a linearly dependent…

Q: Determine if the sets of vectors in Exercise are linearly independent. If for any of these, the…

A: Given: vectors 012, 213, 201   To find: If the given set of vectors are linearly independent or…

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

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Q: The amount of money currently in your bank account is an example of a vector. O True False

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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: Which two vectors are orthogonal if given a =,b = and c =

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Q: Are the following vectors linearly independent? , , ,

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Q: Determine if the vector 2 b = 3 5 can be written as a linear combination of the vectors V₁ = 1 and…

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Q: Determine if the vector is a linear combination of the remaining vectors. Explain the steps.

A: We will check whether the vector v is linear combination of others or not.

Q: Find the length of the vector.v = (2, 0, −5, 5)

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Q: Which of the following sets of vectors are linearly independent?

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Q: 6. What are the advantages and disadvantages of algebraic vectors compared to geometric vectors?

A: Explanation:

Q: Find the length of the vector x = [-2, 2, 6 ]

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Q: 1 If vector is a unit vector, what is the x?

A: We will find the value of x as following.

Q: Show that the vector a= (2, – 5, 3) in V, (R) can not be expressed combination of the vectors a, =…

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Q: Que. 1: Examine the following vectors for linear dependence X, =[1 2 4], X, = [2 -1 3], X, =[0 _1…

A: Write these vectors as rows in the matrix, convert the matrix to echelon form. If the echelon form…

Q: Determine if the given vectors are linearly independent or linearly dependent.

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Q: Determine the vectors axe linear yy independent -3 2. 8. O ON

A: For linearly dependent determinant  of matrix is zero D=0

Q: What must be a if the vectors (1,-a,1,1). (-1,a+2,–2, a –1), (0,2, –1,a² +a-4) are linearly…

A: We have to solve given problem:

Q: Find the largest possible number of independent vectors among 、H-E~目 V1 = V2 = V3 Find any…

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Q: 3. Determine if the vectors linearly independent or linearly dependent Please explain your answer…

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Q: - ()--)- 1 Let a = 2 and b = be two vectors. What is Jal2|b|2 - |a · bl2 ?

A: Here,  Given that  two vectors  . So, we find the value of  |a|^2.|b|^ - |a.b|^2

Q: Find the length of the vector v = (10, 1, 5).

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Q: the vector from P1(1, 3) to P2(4, –2) is

A: Given :

Q: Are the Following Vectors Linearly Dependent or Independent? (3,-2,0,4),(5,0,0,1),(-6,1,0,1),…

A: Vectors v1, v2, v3,..........vn are linearly independent if for scalars c1, c2, c3,.........,cn such…

Q: Show that a set of vectors, which contains a set of linearly dependent vectors, is linearly…

A: To show that a set of vectors, which contains a set of linearly dependent vectors, is linearly…

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.