Show that the vectors v, = (0, 3, 1, -1); vz = (6, 0, 5, 1); vz = (4. –7, 1, 3) form linearly dependent set in R4? Then express V1 in number 3 as linear combination of Vz and V3

Q: Find two vectors of norm 1 that are orthogonal to the vectors u = (2,−3,4) and v = (3,1,−5)

A: The cross product of two vectors is perpenducular to both of the vectors. The cross product of the…

Q: 8. If {V1, V2,..., ,}is a linearly dependent set of vectors, prove that one of these vectors is a…

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Q: Determine k so that the vectors (1, –1, k – 1), (2, k, –4), (0, 2, + k, – 8) in R³ linearly…

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Q: Suppose v, w, z are vectors in R". Show that if r and y are linear combinatio: v, w, and z, then r+…

A: Linear combination of the vectors

Q: Let x and y be linearly independent vectors in R2.If | |x | |= 2 and | |y | | = 3, what, if…

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Q: Find terminal point Q of vector PQ =    <9, −2, 1>   with the initial point at…

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Q: 7. "Let &, n, ở be real numbers and consider vectors (1,5,8²); (1,n,n²); (1,0,0²). Determine the…

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Q: . Find two vectors that are orthogonal to the plane containing the points P = (3,0,1), Q = (4, -2,1)…

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Q: let v = (1, 3, −2) and w = (2, −1, 4). Find all the vectors orthogonal to both v and w.

A: Given: The vectors v=1,3,-2 and w=2,-1,4. To find: The vectors orthogonal to both v and w.

Q: Let V = {ü, v, w} where й 3 ( — 3, 2, — 3), ў — (3, 5, – 5). - Find ũ that would make a DEPENDENT…

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Q: v, =,v, =, v, =

A: To add or subtract two vectors, add or subtract the corresponding components of each vector. For…

Q: 3. Show that the vectors v, = (0, 3, 1, -1); v, = (6, 0, 5, 1); v; = (4, -7, 1, 3) form a linearly…

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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: Define the points P(-4, 1), Q(3, -4), and R(2, 6).

A: The given points are The vector QP is So, the unit vector (v) of QP is

Q: Prove that the set of vectors B = {(1,2,3), (3,2,1),(0,0,1)} is linearly independent and spans R³.

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Q: Find the vector v whose initial and terminal points are given below. (5.4, 2.4), (0.4, –2.6)

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Q: 4

A: We are given the following vectors.

Q: Express the vector from P(-1, -4, 6) to Q(1, 3, -6) as a position vector in terms of i, j, and k.

A: Given vectors are P-1,-4,6 and Q1,3,-6.

Q: Show that the vectors v, = (0, 3, 1, -1); v =(6, 0, 5, 1); v (4, -7, 1, 3) form a linearly dependent…

A: Given vectors v1 = (0, 3, 1, -1); v2 = (6, 0, 5, 1); v3 =(4, -7, 1, 3) . Let c1. v1 + c2. v2 + c3.…

Q: 3. Show that the vectors v₁ = (0, 3, 1, -1); v₂ (6, 0, 5, 1); v =(4, -7, 1, 3) form a linearly…

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Q: 2. Consider the vectors [2, 1, 0, 0], [3, 1,0, 0], [0,0, 0, 1) in R". Find a vector v so that v, (2,…

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Q: Determine whether the given vectors (1, 1,-1, 1), (1,-1, 2,-1), (3, 1, 0, 1) in R* are lincarly…

A: Given vectors are: (1, 1, -1, 1) , (1, -1, 2, -1) , (3, 1, 0, 1) We have to determine whether the…

Q: For what values of m and n are vectors [m,n,1], [2,1,3] and [2,1,1] coplanar?

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Q: 3. Show that the vectors v = (0, 3, 1, -1); v, =(6, 0, 5, 1); v, = (4, -7, 1, 3) form a linearly…

A: Given the three vectors

Q: Suppose that u, ū, and w are vectors in R3 such that ūxi = (2,7, 3) and ūxu = (-5, 4,0). Find: 1.…

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Q: 3. Show that the vectors v = (0, 3, 1, -1); v, = (6, 0, 5, 1); v3 = (4, -7, 1, 3) form a linearly…

A: Given vectors are: v1=(0,3,1,-1), v2=(6,0,5,1), v3=(4,-7,1,3)

Q: Consider the vectors x1 = (8, 6)T and x2 = (4, −1)T in R2. Let x3 = x1 + x2. Determine the length of…

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Q: Suppose v1, ..., vn are linearly independent and Span({v1, .., vn}) = V , then if W ⊂ V and W…

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Q: . Show that the vectors V1=(0, 3, 1, -1); V2=(6, 0, 5, 1); V3=(4, -7, 1, 3) form a linearly…

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Q: 2 3. Show that that the vector u = -5 is a linear combination of the vectors v1 3 2 ------ 2 U2 = -4…

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Q: The terminal point of the vector v = 3i +5j – 4k with initial point (2, –1, 4) is

A: Follow next step

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: Show that v, = v 2 V2 3 span R and express the vector v= as a linear -7 %3D combination of v,,v2.

A: Solve the following

Q: Find a vector that is orthogonal to both v = (1, –2,3) and w = (2, 1, –1).

A:

Q: 20. Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1,-4,0), v = (-1,–1,2,2),…

A: To find two vectors of norm 1 that are orthogonal to the below vectors.…

Q: If u, v are vectors such that |u || - 3, ||v|| - V5, and u v- 1, what is |u + v|| ?

A:

Q: 19. Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1, –4,0), v = (-1,–1,2,2),…

A: Step:- 1 Given that u=2, 1, -4, 0,  v=-1, -1, 2, 2,  w=3, 2, 5, 4 Now, first we check the given…

Q: The set of vectors u = , and u2= are having rank 3 having rank 1 Linearly independent Linearly…

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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: Show that the vectors v, = (0, 3, 1, -1); v, =(6, 0, 5, 1); v; = (4, -7, 1, 3) form a linearly…

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Q: What is the value of each of the constants that are part of the linear combination between the…

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Q: Determine k so that the vectors (1,–1, k - 1), (2, k,-4) and (0, 2 +k,-8) in R linearly independent.…

A: The detailed answer and explanation is given below:-

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

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Q: Find the vector W which is of length 6 and oppositely directed to u = (2,-2,1)

A: Given,          The vector w→ which is of length 6 and oppositely directed to u→=<2,-2,1>.

Q: 2. Consider the vectors [2, 1,0, 0], [3, 1, 0, 0], [0, 0,0, 1)] in R'. Find a vector v so that v,…

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Q: Determine whether the set of vectors Q={(-1,1,1).(-1,0,2).(1,2,3)} spans R'.

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Q: When the set of vectors {u1, u2, . . . , un} is linearly independent and the set {u1, u2, . . . ,…

A: We have given; The set of vectors {u1, u2, . . . , un} is linearly independent and the set {u1, u2,…

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

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Q: 3. Show that that the vector u = |-5 is a linear combination of the vectors vị = |-3 3 2 V2 = -4 and…

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Q: The vector 1 is in Span{ V2, ., Vm } if and only if ( V1..., Vm ) are linearly dependent. O True…

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