Can 5= (7,14,0) be written as a linear combination of vectors from the set {(1.-2,-1). (0,1,2). (3,-1,0)} ? If yes, clearly show how the coefficients are calculated (trial and error will not be accepted). If no, then explain why not. Determine with explanations and calculations whether the set {(-2,3,0). (1, –1,2). (0,3,2)} is linearly independent

Q: The vectors (3,-4,1) and (5,3,3) are orthogonal. True False

A: Topic - vector

Q: If possible, write the vector w as a linear combination of the vectors V₁, V2, ..., Vk. If it is not…

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Q: Write the vector (-5, -9) as a linear combination of the vectors (-2, 3) and (1, 4).

A: NOTE: Refresh your page if you can't see any equations. . write both vectors in the matrix and the…

Q: Write the vector (2, –3) as a linear combination of (2, –1), (–1,2) Select one: O 2/5(2, –1) +…

A: We need to find the linear combination of the given vector. NOTE - all the options given are wrong.…

Q: Determine whether the set of vectors is orthogonal. 4 2 - 4 -4 - 3

A: To determine Whether these sets of vectors are orthogonal or not.

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

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Q: Let w= (-1,4,15), v = (1, 2, 8), v = (3, 0,1). Does w belong to span(v,,v,)? If yes, then write the…

A: We will find out the required solution.

Q: Find the vector PP, 1. Р.(3,2) P, (5,7) 2. P(-2,-1) 3. Р (3,3) P,(4,-5) P, (5,5) 2

A: As per our guidelines we are suppose to solve only first three sub-parts of a question. Kindly…

Q: What is the component form of the position vector for a vector with an initial point of (-1,0) and a…

A: We have to find component form of position vector.

Q: 8. Write the vector (5,6,0) as a linear combination of the vectors (-1,2,0), (3,1,2), (4,–1,0) and…

A: We have to write the vector (5, 6, 0) as a linear combination of the vectors (-1, 2, 0) , (3, 1, 2),…

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

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Q: Suppose the solution set of a certain system of equations can be described as x1 = 5 – 4t, x2 = -6 –…

A: Given solution set is x_1=5-4t, x_2=-6-2t ,x_3=4t-5 ,x_4=3t-3 . Now we will use the vector notation…

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: 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: Hello, any help for this problem would be greatly appreciated. Thank you! 7.3

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Q: There are four vectors (1,2,3), (1,-1,2), (2,4,6) and (2,6,c). If there is a condition in which the…

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Q: If possible, write the vector w as a linear combination of the vectors V₁, V2, ..., Vk. If it is not…

A: a) Given:     w=1,1,5, v1=7,7,7      v2=2,5,3, v3=4,1,-1 w=i^+j^+5k^, v1=7i^+7j^+7k^…

Q: Let v1 = (-6, -6, -9), i2 = (3, 3, 12), iz =(-1,-1,6). Are the vectors v1, 02 and vz linearly…

A: See the attachment

Q: Find the Values of for which vectors linearly dependent the are -3 4 -5 8. 6. - 2 6. -8

A: Given that three vectors are linearly dependent.

Q: Write the vector (7,8, –8) as a linear combination (if possible) as of the vectors (-1,1,2), (2,3,…

A: See answer below

Q: Find the vector v = PQ. Р- (2, 1,4) Q = (-8.25, -4.25, 8) v =

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Q: 2) Subtract the (2) vectors; (4, 6) & (-8, -10)

A: The given vectors are 4, 6 and -8, -10 We need to subtract the given vectors.

Q: The normal vector of 2x + By - 16.7z = -8 is: ○ [2, 뮤, -16.7, 8) ① [호, 꽃, 16.7, -8] ① [올, 꽃, -16.7]…

A: We have given equation of a plane  92x+133y-16.7z=-8 Comparing this with the equation  lx+my+nz=d We…

Q: Find the vector that has the same direction as (3, 2, -6) but has length 5.

A: Just follow the flow and you are done.

Q: Find a vector that has the same direction as (-4, 6, 4) but has length 6.

A: we have to find a vector that the same direction as <-4, 6, 4> but has length 6

Q: Express the vector (-1,5,-6) in R^3as a linear combination of (2,0,7),(2,4,5) and (2,-12,13).

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Q: 1. Find the sum of the vectors (3,-1) and (-1,5) and illustrate geometrically.

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Q: A rocket is equipped with a propulsion system consisting of three thrusters. Each of the thrusters…

A: This is a problem from vector space so I used various operation such as row reduction to solve the…

Q: Are the vectors –2 – 8x + 4x², – 4 – 12x – 20z² and -4 – 14x - 6x² linearly independent? choose If…

A: Given three vectors are: −2−8x+4x2, −4−12x−20x2, and −4−14x−6x2 To determine whether the vectors are…

Q: 7. Find all values of x that make (x, 1, –3) and (x, 2, x) perpendicular vectors.

A: I am attaching image so that you understand each and every step.

Q: Express i = (3,7,-4) as a linear combination of i = (1,2,3), ỷ = (2,3,7), z = (3,5,6), also check…

A: see below the answers

Q: How many Linearly Independent vectors in the set {(1, 1, 1, 2), (1, -1, 2, 3), (3, 1, 4, 7), (2, 2,…

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Q: Determine which vectors that are orthogonal to (– 3, -6)? (-4,2) and (-1,3) (-10, 5) and (-3, 6) a.…

A: To determine the vectors which are orthogonal to -3,-6. (a) Given vectors are -4,2 and -1,3. We know…

Q: 4 2. Decide whether the vectors (1, 2,0,-1], [2, 6, -3, -3], [3, 10, -6,-5] are linearly…

A: Given vectors are ,  [ 1,2,0,-1 ] ,  [ 2,6,-3,-3 ] ,  [ 3 ,10 ,-6 ,-5 ]  (.)  The given vectors are…

Q: Are the vectors -1, 3z-2z and-2z - linearly independent? choose If the vectors are independent,…

A: The objective is to determine whether the vectors -1,-3x-2x2 and -2x-x2 are linearly independent or…

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

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Q: Hi, any help on this problem would be greatly appreciated. Thank you!

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Q: (3,-2,1) can be written as a linear combination of which of the following vectors? 2, 0, 0), (0, 1,…

A: The vector (3,-2,1) can be written as linear combination of the vectors in (a) and (c).

Q: Write the vector (7, 8, -8) as a linear combination (if possible) as of the vectors (-1, 1, 2), (2,…

A: Let the linear combination be, x-112+y23-2=78-8 It is required to determine the value of 'x' and 'y'…

Q: (4, 3), (4, -3), (-3, 4) and  (-3, -4). Which of the following pairs of vectors is perpendicular?

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Q: The set of vectors {(1,1,0,0),(0,-1,0,0),(0,0,1,1),(1,0,1,1)} is linearly dependent. What is a valid…

A: The set of vectors {(1,1,0,0),(0,-1,0,0),(0,0,1,1),(1,0,1,1)} is linearly dependent

Q: - Find the length of the vector -3v if v = (2, 3, -2, 1).

A: Givenv=(2,3,-2,1)-3v=(-6,-9,6,-3)

Q: Is it possible to write the vector (-5,11,-7) as a linear combination of the vectors…

A: See the attachment

Q: Suppose that ú, v and w are any three vectors in some R". Show that the set of three vectors: S =…

A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…

Q: The vectors (-3,4, -1) and (3, -4,1) are orthogonal. True False

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Q: Write the vector (7, 4,-12) vectors (-2, 1, 2), (1, 1, –2) as a linear combination (if possible) as…

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Q: If vector (3,2,2) is expressed by a(1,1,-1)+b(0,1,3)+c(1,-1,1), what are the values of a, b, and c ?

A: Given : Vector (3,2,2) is expressed by a(1,1,-1)+b(0,1,3)+c(1,-1,1). That is

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 vectors (-1, 2, – 1) and (2, –4, 2) are parallel and not orthogonal. True False

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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.