Let the set {V1, v2} be linearly dependent. Determine whether the set {v, + 4v2, 2v, – v2} is also linearly dependent by solving the equations a(v + 4v2) + b(2v, - v2) = 0 and cv + dv2 = 0 for scalars a and b in terms of scalars c and d, where c and d are not both zero. a = b = Is it possible for both a and b to be zero? O Yes O No Thus, is the set {v + 4v2, 2v - v2} linearly dependent? O Yes O No

Q: 2.x - y-z = 0 5x - 2у +2: 3 Зх + у - 2: -8

A:

Q: (b) x1 + x2 + 2x3 = 5 + x3 = -2 2x1 + x2 + 3x3 = 3 %3D X1 %3D %3D

A: We see from the given system that, if we add first two equations, we will get the third equation.…

Q: Show that V1, V2, V3 are linearly independent, but V₁, V2, V3, V4 are not. Then express V4 as a…

A:

Q: Find all values a for which the set {(a — 5, 13, 0), (−1, a – 9,0), (4, 0, a — 2)} is linearly…

A:

Q: Determine: If S = {X2,1 + X2} is linearly independent or dependent.

A:

Q: ) Let B = {vi =,₂ =, V3 =}. Determine whether B is linearly independent or linearly dependent.

A: Let us consider a set of vectors V=v1,v2,.......vn. The set of vectors are said to be linearly…

Q: Show that vectors (86, 87, –46), (-8, –6, –2), and (-6, –7, 6) are linearly dependent-that is, there…

A: If vectors are linearly dependent then they can be expressed as a linear combination of each other

Q: Find the scalars if they are linearly dependent.

A:

Q: Write b as a linear combination of the vectors v1, v2, and v3,  where: (view attachment)   Set up…

A:

Q: ether the set of vectors in P2 is linearly independent o {2 – x - 4x2, 3+ 6x + 2x?, 2+ 10x – 4x?} ||

A:

Q: The vectors 3 -4 3 = 12 w = -8 5 -23 + k 7 are linearly independent if and only if k +

A: Solution:-

Q: 3. Determine whether the vectors are linearly independent or are linearly dependent in P2. 1+3x+ 3x,…

A:

Q: Find the maximum and minimum values, and a vector where each occurs, of the quadratic form subject…

A:

Q: Let {u₁, 12, 13} be a linearly independent set of vectors. Select the best statement. {u₁, U2, U3,…

A:

Q: Show how v is orthogonal to any linear combination formed by w1 and w2

A:

Q: linearly independent If they are linearly dependent, find scalars that are not all zero s linearly…

A:

Q: 3 3. Let V = 5. Find vectors b₁, 62, 63 such that is a linear combination of b₁, b₂, b3. Additional…

A:

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

A: