Let S = {v1, v2, v3} be a set of linearly independent vectors in R^3. (a) Are the vectors in the set T1 = {v1, v1 + v3, v3} linearly independent? Show how you arrived at your answer. (b) Are the vectors in the set T2 = {v1 − v3, 3v1 + v2, v2 + 5v3} linearly independent? Show how you arrived at your answer

What helps to set of vectors linearly independent?

Define' a vector to contain 2 components: (a,b) where a a rational number, b is an irrational number. Let S? be a set that contains such vectors, ie. s*={ (a,b)| for all rational numbers a, irrational numbers b}. For example, (3.14,71) is in S², but (e,71) is not in S² – 1 & e are well known math constants. Is S a vector space over the integers?

Let V₁, V2, V3 be the vectors in R³ defined by 18 ---D V₁ = -6 V2 = -14 V3 = 20 (a) is (V1, V2, Vs} linearly independent? Write all zeros if it is, or if it is linearly dependent write the zero vector as a non-trivial (not all zero coefficients) linear combination of V₁, V₂, and V3 0 (c) Type the dimension of span {V1, V2, V3}: Note: You can earn partial credit on this problem. -25 -18] 0=v₁+√₂+vs (b) Is (v1, vs} linearly Independent? Write all zeros if it is, or if it is linearly dependent write the zero vector as a non-trivial (not all zero coefficients) linear combination of V₁ and V3. 0=v₁+v₁ V3

Let v1=[-2,2,1], v2=[-8,7,4], v3=[-29,25,14], w=[6,6,1] is W in {v1,v2,v3}? how many vectors are in {v1,v2,v3}? How many vectors are in span {v1,v2,v3}? is w in the subspace spanned by {v1,v2,v3}?

My rectangular cabbage patch has a total area of 115 sq. ft. Find its perimeter in terms of the width x.