Show that the vectors (x1, Y1) and (x, 2) in V, (F) are linearly dependent if

Q: If a vector u is orthogonal to vectorsx and y then u is orthogonal to the vector x + y.

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Q: 9

A: We need to determine all the values of the constant a for which the vectors

Q: let ej denote the vector whose jth coordinate is 1 and whose other coordinates are 0. Prove that…

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Q: In Fn, let ej denote the vector whose jth coordinate is 1 and whose other coordinates are 0. Prove…

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Q: 2. Choose the linearly dependent vectors in R

A: two non zero vectors V1, V2 are said to be linearly independent if and only if aV1+bV2= 0 ⇒ a=0 and…

Q: * Find the values for h for which the vectors are linearly dependent: 7

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Q: Determine whether the vectors (4, 2, 3)T , (2, 3, 1)T , and (2,−5, 3)T are linearly dependent.

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Q: Express the vector t as a linear combination of the vectors u, v and w: t = (5,30, –21), u = (5,2,…

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Q: 2. Show that if the vectors v,, v2, .,Vm are mutually orthogonal then they are linearly ...…

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Q: Let f(x, y) = 5y² In(4x). Then Duf(1,4) in the direction of the vector (-2,-2) is

A: The explanation of answer as follows

Q: 1 Y

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

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Q: Show that a set of vectors {v,, v2. ..., V5} in Rn is linearly dependent when dim Span {v,, v2, ...,…

A: We need to show that: {v1, v2, v3, v4, v5}  in Rn are linearly dependent when  dim Span{v1, v2, v3,…

Q: What is the resultant of vectors a and b? ( A ) GL B

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Q: If is a covariant vector in Cartesian coordinates x',x2.

A: In this question, we have covariant tensor (x1x2,x2x1) By using the transformation cartesian to…

Q: (d) Suppose the three vectors x, y, z E R³ are known to be linearly independent. Are the three…

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Q: Let x,y,z be (non-zero) vectors and suppose that z=4x−4y and w=12x−12y−4z. Are the following…

A: A vector is a span of vectors when the first one can be written as the linear combination of the…

Q: Find a non-zero vector v perpendicular to the vector u = [ -1 ]                          [ 8 ]

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Q: Determine whether the vectors cosx, 1, and sin2(x/2) are linearly independent in C[−π,π].

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Q: Find a vector that is orthogonal to v =〈1, 2, 1〉 but not to w =〈1, 0, -1〉

A: Given: Find a vector that is orthogonal to v =〈1, 2, 1〉 but not to w =〈1, 0, -1〉

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

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Q: Let x=⟨1,1,1⟩ and y=⟨0,3,−2⟩Find a unit vector that is orthogonal to both x and y

A: If w is an unit vector which is orthogonal to x and y, so

Q: Two linearly independent vectors in R3 span R2, is that true

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Q: Г 13 and vz = 14 are linearly independent. Determine whether the vectors v 14

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Q: Find a vector v→parallel to the intersection of the planes 3x+y+2z=3 and       −(x+2y+4z)=7

A: Vector parallel to intersection of two planes is cross product of the normal vectors of the two…

Q: Find a non-zero vector x perpendicular to the vectors  v= [-3]    And u = [-1]      [11]…

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Q: ^2

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Q: Let x 0 and y 0. (a) If xly, show that {x, y} is a linearly independ- ent set. (b) Extend the result…

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Q: write the equation of the plane with normal vector n passing through the given point in the scalar…

A: Given, Normal,n=(2,-4,1) Point, P=13,23,1     Find the equation of the plane with normal vector n…

Q: The plane through the origin that contains the vectors i - j and j - k

A: Given vectors are i - j and j - k. The plane is passing through given vectors i.e. 1i - 1j+0k and…

Q: Find a vector x = ( c, d) that has dot products x · r = 1 and x · s = 0 with two given vectors r =…

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Q: The vectors w = x= y = and z = are linearly independent. O linearly dependent. If the vectors are…

A: The solution is follows:

Q: Find nonzero vectors u, v, w that are perpendicular to (1, 1, 1, 1) and to each other.

A: Then   -------------(1) Also  --------------------(2)

Q: Realize the Cauchy-Schwarz inequality for the vectors x= ( -1, 2, 4,3), y=(0,-2,1, 4) ∈ R4 and find…

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: 4. Show that the vectors v1, v2, and v3 are linearly dependent, where Vị = V2 = and v3 =

A: If we have a set of vectors v1, v2, v3, ..., vn, then they are said to be linearly dependent if…

Q: Let x = (1,2,3) and y = (1,1,1) Project y on x (in econometrics, this may be denoted by Px). Are the…

A: We will first write the formula for projection of a vector onto another vector b .

Q: If X and Y are linearly independent vectors in R", then {0,X,Y} is linearly independent.

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Q: Find basis for the set of vectors in R2 on the line y= nx . where n=9.

A: Explanation of the solution is given below...

Q: Let f (x,y,z) = xye² + yze*. From point (1,0,1), which unit vector points in the direction in which…

A: Consider the given information. fx,y,z=xyez+yzex The point is 1,0,1. The direction in which f…

Q: Is it always true that T(0) = 0 where the zero vectors live in the appropriate spaces? Justify

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Q: Find a vector function that represents the curve of intersection of the paraboloid z = x^2 + y^2 and…

A: Intersection of paraboloid and cylinder can be obtained by representing y in the form x and z in the…

Q: Exercise 6 Is the set of vectors V = {i² + 2t – 1,3t + 5, -t² + t + 6} linearly dependent?

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Q: Find x if the vectors a =i+j+ 2k;b = xi-j+k; coplanar or linearly dependent.

A: Given,       a=i+j+2kb=xi-j+kc=3i-2j-k

Q: Determine all values of the constant k for which the vectors and are linearly dependent.

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Q: Show that if u and v are linearly independent vectors, then so are  u + v and u -v.

A: Given :           u and v are linearly independent vectors.   To prove :               u + v and…

Q: Show whether the vector w is a linear combination of vectors v1, v2 and v3 where --I --E --4 -- w =…

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Q: Give a set of vectors that is linearly dependent for P3 Show your work.

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Q: Determine if the vectors of R³; vị = (1, –3,0), v2 = (3,0,4) and vz = (11,–6,12) are linearly…

A: Given vectors are: v=(1,-3,0) v=(3,0,4) v=(11,-6,12) Form a matrix by having rows as given vectors.…

Q: Write y as the sum of two orthogonal vectors, x1 in Span{u} and x2 orthogonal to u

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Q: Find two linearly independent vectors perpendicular to the vector i = |3

A: to find linearly independent vector perpendicular to vector v→=139 solution let X=x1x2x3 as we know,…