ii) Show that any four vectors oj, , 5, Vi in R are linearly independent.

Q: If v1, v2 E R³ are linearly independent vectors and v3 ¢ span{v1, V2} then {v1, v2, v3} must be…

A: We have to check linearly independent

Q: Suppose A and B are non-zero vectors in R. If A•B = 0, then A and B are parallel. True False

A: Follow next step

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

A:

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

A:

Q: Every orthogonal set of vectors is linearly independent. O True O False

A:

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: u = (2, 3,-1) v= (0, 1, -2) w = (2, 4, -3).

A:

Q: Show that the vectors V1 = ( 1, 1, 2, 4 ), V2 = ( 2, -1, -5, 2 ), V3 = ( 1, -1, -4, 0 ) and V4 = (…

A:

Q: Suppose that the vectors {v, u, w} are linearly independent in some vector space V. Prove that the…

A: Given that the vectors u, v, w are linearly independent in some vector space V. Then the linear…

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: Consider the vectors x1 = (8, 6)T and x2 = (4, −1)T in R2. Determine the length of each vector.

A:

Q: Determine whether the set of vectors in P, is linearly independent or linearly dependent. S = {1 +…

A:

Q: Show that there are no vectors u and v such that 11u 11= 1, ||v|| = 2, and uxv= 3.

A: If u and v are two vectors, and the angle between these two vectors is θ Then the magnitude of the…

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

A:

Q: Let u, v, and w be linearly independent vectors. Show that (u+v), (u-v), and (u-2v+w) vectors are…

A:

Q: 5. Suppose us v and w are linearly independent vectors. Prove that (i) и+у - 2w, и — v — w, и+ w are…

A:

Q: at vectors （c1 - a1, c2 - a2）and （b1-a1,b2-a2）are linearly depend

A:

Q: 1. Show that the necessary and sufficient condition for two nonzero vectors A and B to be…

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: Prove that if the vectors a,b parallel, then āxb=0. are %3|

A:

Q: Suppose that u and v are vectors in 3-space such that u ||= 5 and u · v= 7. Find: (a) u · u = (b) v…

A:

Q: Show that if {V1, V2} is a linearly independent set of vectors and v3 does not lie in Span {V1, V2},…

A:

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: Let nonzero vectors ū,v,weR be linearly independent. Show that there does not exist a nonzero vector…

A:

Q: Prove that two vectors v = (a, b) and w = (c, d)are perpendicularif and only if ac + bd = 0

A: We prove the above statement using the concept of dot product or scalar product of two vectors. The…

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

A:

Q: 11) in triple cross of vectors (A × C) × B = Cx (B × A).

A:

Q: Determine whether the vectors v, = 1 10 and 11 are linearly %3D V3 independent.

A:

Q: Determine whether the set of vectors in P, is linearly independent or linearly dependent. S = {1 +…

A:

Q: -2 Show whether or not the vector bs is a linear combination of the vectors a, = az = and az = that…

A:

Q: Show that if u and v are vectors in the three-space, then ||u x v||? = ||u|| ||||² – (u · v)²

A: u and v are vectors.

Q: If the vectors b, c, d are not coplanar, then can we say that the vector (ā×b)×(ē×d) + (ā×ē) × (dxb)…

A:

Q: 1. Consider the vectors [2, 1,0, 2), [3, 1, 0, 1), [1, 1,0, -1) in R. Decide whether they…

A:

Q: 2. Suppose that u, v and w are vectors in 3-space such that ||u|| = 5, u·v = 7, and u · w = -3 а.…

A: Answer

Q: Determine whether the set of vectors in P, is linearly independent or linearly depenc S (-2- x, 2 +…

A: The vectors v1,v2,....vk are linearly independent if a1v1+a2v2+...anvn=0 where all ai=0 The vectors…

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: Show that the vectors X1 = 2e2t and 2et X2 5e3t form a linearly independent set.

A:

Q: Show that if C is any two-dimensional vector then it can be written as a linear combination of the…

A: Given: C→ be any two dimensional vector spaceie.,   C→=x,y|x,y∈ℝFormula: Convex set∃ t,s∈ℝ such that…

Q: Let a = 2i and b = -2i + 3j be two-dimensional vectors. Compute la – b|.

A:

Q: 4. Determine whether the vectors a = 2i – 3j+ 5k, b = 3i+j – 2k and c =i- 7j +12k linearly dependent…

A: To check whether the vectors are linearly dependent or linearly independent.

Q: Determine whether the set of vectors in M2,2 is linearly independent or linearly dependent.

A:

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: Suppose that u and v are vectors in 3-space such that |u||= 5 and u · v = 7.

A:

Q: Let y = and u = 3 Write y as the sum of two orthogonal vectors, one in Span {u} and one orthogonal…

A:

Q: 3. Consider two vectors v = and w =. (a) Decide if v and w are linearly independent.

A: (a) Given v = <0, 1, 2>  and  w = <1, 0, 1> Let av + bw = 0 => a(0, 1, 2) + b(1, 0,…

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

A:

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: IH A and B are any two vectors in V, prove that (A- B) x (A + B) = 2(A X B).

A:

Q: 64. Show that if u + v and u – v are orthogonal, then the vectors u and v must have the same length.…

A: here, the given vectors, A =u+vB=u-v given that, they are orthogonal, that is, A·B=0u+v·u-v=0⋯⋯1

Q: Prove that two vectors are linearly dependent (taken as a set of vectors) if and only if one vector…

A: Let X and Y be two vectors. Suppose these two vectors are linearly dependent. [To prove: One vector…