2. Determine whether the vectors span the vector space. Explain your answers. (a) The vectors u = (1,3) and v = (3, 12) in R². (b) The vectors vị = (1,1,1), v2 = (0,0,2), and v3 = (0,0, –1) in R³.

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

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Q: Find a non-zero vector a perpendicular to the vectors [3] and ū = 2 1

A: Given, v→ = 372  and  u→ = 121   We have to find the non zero x→ vector perpendicular to both the…

Q: Find a nonzero vector orthogonal to the plane through points P(2,1,5), Q(-1,2,3), and R(0,3,3), and…

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Q: Find eguation of a Plane that an contains the vector: and and Z=3E

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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: a) If possible, express w as a linear combination of vectors u and v. w = - (1,0, —7), и %3D…

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Q: Determine whether the vectors u = (2, –1,3), v = (4,1,2), and w = (8, – 1,8) span R³. If not find…

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Q: (a) Using Gaussian elimination, find a vector v such that

A: As per our guideline is multiple questions are posted we are supposed to answer only the first one.…

Q: Consider the vectors a = (-1,–2, 3), b = (3,0, –2), v = (2, –5, –4) and the plane P given by 2x + y…

A: The given vector is; a→=-1,-2,3b→=3,0,-2v→=⟨2,-5,-4⟩and Plane P is;2x+y=z+13⇒2x+y-z=13…

Q: Consider the vectors u =(1,9,4) and v =(-16,0,-4).| The vector W" =(x,0,z) that simultaneously…

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Q: The norm of the vector v = (-4, 4, -5, -3) is O y66 O 30 O y6I 66 O 61 O y30 O7 O None of the other…

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Q: (c) Are the vectors = (3, 1, 2, 1), v2 = (-1,0,1,0), 03 independent? Explain why. (3,0,0,3), v4 (5,…

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Q: Find a vector, v, in component form, that is orthogonal to the plane containing the points P = Q =…

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Q: (a) Determine whether the vectors vi = (1,1,2), v2 =(1,0,1) and v3 = (2,1,3) span the vector %3D %3D…

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

A: Given vectors are: v=123; u1=110; u2=011 If the vector v is a linear combination of the remaining…

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: Verify the Pythagorean Theorem for the vectors u and v.u = (4, 1, −5), v = (2, −3, 1)

A: Given   The vector u = (4, 1, −5), v = (2, −3, 1) Pythagorean Theorem for the vectors

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: Q1. If O (0,0,0) in (x,y,z) 3-D space and r(2,5,1) draw the vector in 3D and find its direction.

A: Plot point in 3D

Q: Write the vector x=0 as a linear combination of the vectors u=0, v= 1, w= 1 1

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Q: Define irrotational vector. Is the vector A =(6xy+z³)i+(3x² - 2)j+(3xz² – y)k irrotational? Justify…

A: we have the vector A=(6xy+z3)i+(3x2-z)j+(3xz2-y)k we have to check weather the given vector is…

Q: Find a vector v that is perpendicular to the plane through the points A = (4, – 5, –2), B = (2,3,…

A: We are asked to find the vector that perpendicular to the plane through the points

Q: Find a vector v that is perpendicular to the plane containing 3 -() 6 and 0 2

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Q: 4. Show how to find a vector ẽ = c – Ab that's perpendicular to b and is a linear combination of b…

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Q: Let the vector be x = (5,6), determine its coordinates relative to the base B = {(1,1),(-1,2)}}

A: Introduction: When a basis is provided, one can represent a vector belonging to the precise vector…

Q: Find the unit vector u in the di rection of the vector v=2(2, 1, 2).

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Q: V. 3. V3

A: We have to solve given problem;

Q: () 1 (b) Find the length of the component of the projection of the vector a = vector 6 = 2 () onto…

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Q: Q2: Determined the component of the vectors at each point…

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Q: Find a vector w perpendicular to both vectors u=2i-j+2k and v=3j-4k w=i+2j-3k w=-2i+8j+6k…

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Q: a. Please provide a well explained answer for the follwoing. And explain what are the components of…

A: Components of vector  In two dimensional ,any  vector can divide into two components x -…

Q: Find the vector z, given that u = (3, 2, 9), v = (2, 2, -1), and w = (4, 0, -4). %3= z = u - v + 2w

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Q: (a) Give examples of three distinct vectors vị, v2, vz in the vector space R³ such that vz E…

A: Let v1 = {1,1,1}v2 = {2,3,4}v3 = {1,2,3} Here  v2 = {2,3,4} = {1,1,1}+{1,2,3} = v1+v3

Q: Determine whether the vectors u = (2,–1,3), v = (1,1,–2), and w = (3, –1,5) span R. If not find the…

A: To Show : the vectors u→=2, -1, 3, v→=1, 1, -2, w→=3, -1, 5 span ℝ3 or not   Consider a linear…

Q: Find a vector perpendicular to the plane of P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2)

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Q: Use vectors =(-1, 1), v= (7, –2), and w= (0, 4) to find (u w)v, and determine whether the result is…

A: We can answer it as below

Q: 5b- За Let W be the set of all vectors of the form Find vectors i and v in R such that W = span {i,…

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Q: Let vectors u=[1,0,-1] and v=[-2,1,2].Find the vector w that is orthogonal to both u and v

A: The given vector is u=[1,0,-1] and v=[-2,1,2]

Q: Find a non-zero vector 7 perpendicular to the vector u = 5= [8]. 6

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Q: 5. Find a nonzero vector orthogonal to the plane through the points P(1,0, 1), Q(-2, 1, 3), and R(4,…

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Q: For the vectors u (1,0, 1) and v (0, 2, 1), u x v = %3D O A. (1, 2, 0) O B. (1, 2, -2) OC. (2, 1, 2)…

A: Given. The vectors u = 1, 0, 1 v = 0, 2, 1 We have to find u×v

Q: determine projection of the vector b = -1 1 1 on the space generated by the vectors {--E)--[ -[+]}…

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Q: Which of the following vector is perpendicular to the plane 2x - 3y + 5z +7 = 0? O1-6, 1, 3] O [2, -…

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Q: 32. a) Determine the vector equation of the line of intersection of these 2 planes: x + 2y + 2z = -3…

A: According to Bartleby guidelines I can only answer the first question of the given two problems.

Q: (c) Are the vectors v1 = (3,1,2, 1), i2 = (-1,0,1,0), iz = (3,0,0,3), T4 = (5, –2,0, 4) linearly…

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Q: 2a)Use triple scalar to verify that the following vectors are not coplanar. a=[-2,1,0], 5=[-3,4,5],…

A: Given problem:- 2a)Use triple scalar to verify that the following vectors are not coplanar.…

Q: (a) Find a vector perpendicular to the plane that contains the points P(1, 0, 0), 0(2, 0, – 1), and…

A: It is given that the plane contains  P(1,0,0), Q(2,0,-1) and R(1,4,3). Let, Equation of plane…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.