show that the vectors V₁ = (2,0,- 2, 1) > V₂ = (3,1, -5,0) and V3=(2, 2, -6, -2) form Linearly defendent set in R4 and express each vector as a linear Combination of others

Q: define (2a - b + 4c, 3a-c, 4b + c) as a linear combination of three nonzero vectors

A: We have to define  (2a - b + 4c, 3a - c, 4b + c) as a linear combination of three nonzero vectors

Q: If x is an n-vector, show that x + 0 = x.

A: Given, If x is an n-vector.

Q: Show whether or not the set of vectors B = {U, V, W} where U = V = and W = 0 is a basis for R³.

A:

Q: Find the length of the vector x=x= |x|=|x|=

A:

Q: Construct a vector that is perpendicular to the plane containing (−2, 4, 1),(3, 3, -1) and (1, 0,…

A: Construct a vector that is perpendicular to the plane containing (-2,4,1),(3,3,-1) and (1,0,2)

Q: Express the vector p = (-6,15,-3) as linear combination of the vectors u = (1,-1,3), v = (2,-5,0)…

A:

Q: 5) Find a vector in component form that is orthogonal to the vectors a = (9,3,-7) and b = (10,-8,2)

A:

Q: Find a maximal set of linearly independent vectors out of the set {v1 = (1,2, 3, 4), v2 = (2, 3, 4,…

A: From given set of vectors we have to find maximal set of linearly independent factors. Concept: Let…

Q: why is it not all 4 vectors span W?

A: Lets look at how span of a set is defined :

Q: If possible express the vector v as a linear combination of V1, V2, and V3. (b) v = (0, 0, -1), V₁ =…

A:

Q: Let V₁, V2, V3 be the vectors in R³ defined by 18 ---A V2 = -14 (a) Is (V1, V₂, V3} linearly…

A: We now solve this questions

Q: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

A:

Q: Let the following vectors be in R³ a = (1,3,-1) b = (-2,1,3) c = (3,2,1) d= (1,-1,2) 14.- Perform…

A:

Q: Prove that swapping the order of vectors in the cross product changes the sign of the output: ьха3 -…

A: