A set of 3 vectors in IR^4 spans IR^4. Is this true or false?

Q: express the vector (4,5,5) as a linear combinations of vector (1,2,3) (-1,1,4) and (3,3,2)

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

A: Topic - vector

Q: Find the sum of the vectors (–1,4) and (6, –2) and illustrate geometrically.

A: A vector V→=a,b can be represented on the cartesian plane, From the vector law of addition,…

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: 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: Definition used -                       If we have to write a vector as a linear combination of…

Q: Find area of triangle whose vectors Р (3,3, 1), Р2-1,0,2), Р3(2,3,3)

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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: State two important features for a set of orthonormal vectors

A: A set of vectors forms an orthonormal set if all vectors in the set are mutually orthogonal and each…

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: Express the vector (-1, 0) as a linear combination of the vectors (-1, - 1) and (-1, 1). (-1,0) =…

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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 orthonormal. If the set is only orthogonal, normalize the…

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Q: Which one of the sets of vectors (given in Matlab notation) is linearly independent?

A: Note:  checking by matrix   if  zero vector is in the set then set is linearly independent

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: Suppose vector a= (4, -6, 10) and vector B= (-6, 9, -15). What is a x b?

A: topic - vectors

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 of length 5 that is orthogonal to both vectors ⟨4,−1,0⟩ and ⟨−3,2,−1⟩

A: The vector orthogonal to two vectors u,v is = ± (u×v)/ |u| |v| Here u =  ⟨4,−1,0⟩ , v =…

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: 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: 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: Sketch the given vector with initial point (4, 1). u = (-5, 3)

A: Here we have to plot the given vector.

Q: What is the component form of the vector with an initial point of (-2,5) and a terminal point of…

A: Given that ,  The vector with  Initial Point = (-2 , 5) Terminal Point = (7 , -3).

Q: s the set of the vectors (:). (2) 1 ) --(;) --() u2 4 U3 = 1 1 1 rthogonal? What is the expression…

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Q: Show that the vectors are orthogonal.

A: Given vectors are u=<u1, u2>=<4, -1>v=<v1, v2>=<2, 8>

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 two unit vectors orthogonal to both (5, 8, 1) and (-1, 1, 0). (smaller i-value) (larger…

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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: 2 Determine the tail of the vector 4 whose head is (3, –2, 2).

A: To determine- The tail of the vector 24-1 whose head is 3-22.

Q: Determine if the vectors (2, –2, 1) and (0,1, 2) are orthogonal.

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Q: Express the vector v with initial point P and terminal po P(-9, -7), Q(-3, -3)

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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 whether Hhe Lindependent. by inspection Vectors are linearly 6. -2 -3

A: A vector is given

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

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Q: Explain the Combination of basis vectors.

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Q: Are the vectors u=(1,2,-4), v=(-5,3,-7) and w =(-1,4,2) are in the ?same plane

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

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Q: Create a column vector with 14 equally spaced elements in which the first element is 3 and the last…

A: Arithmetic Progression:                          an=a1+n-1d where an= the nth term in the sequence…

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

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Q: 1) Add the (2) vectors; (2, -6) & (-3, 8)

A: The given vectors are (2,-6) & (-3,8). We need to find the addition of the given vectors.

Q: Prove that swapping the order of vectors in the cross product changes the sign of the output: ьха3 -…

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Q: find two unit vectors orthogonal to (-1,-1,5) and (-5,-,3,3)

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Q: Explain how to add vectors.

A: vector:  a quantity which has magnitude along with direction is a vector. vector addition:…

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

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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.