Consider the vectors v⃗ = 〈6,4,0,6〉, v⃗ = 〈4,−3,5,3〉, and v⃗ = 〈−3,0,4,7〉.123
Is the vector w⃗ = 〈13, −8, 32, 39〉 in span({v⃗ , v⃗ , v⃗ })? If so, find the scalars that form the
linear combination.
Consider the vectors v⃗ = 〈6,4,0,6〉, v⃗ = 〈4,−3,5,3〉, and v⃗ = 〈−3,0,4,7〉.123 Is the vector...
3 Span Here is a list of four vectors: 1000 Is the vector 4 in the span the first four vectors? If it is, exhibit a linear combination of the first four 1-2 vectors which equals this vector, using as few vectors as possible in the linear combination.
(3) Determine which of the following sets is linearly independent. 02-1 (a) If the set is linearly dependent, express one vector as a non-zero linear combination of the other vectors in the set. (b) If the set is linearly independent, show that the only linear combination of the above vectors which gives the zero vector is such that all scalars are zero. (c) For each of the sets, determine if the span of the vectors is the whole space, a...
Question 4 [10 points) Consider the following vectors: a= For each of the following vectors, determine whether it is in span{a,b,c). If so, express it as a linear combination using a, b, and c as the names of the vectors above. V1 = <Select an answer > < Select an answer > Vy is not in span{a,b,c} V1 is in span{a,b,c} <Select an answer > anotomon V3 = <Select an answer >
Consider the following vectors: 2 2 2 10 -3 For each of the following vectors, determine whether it is in span (a, b, cj. If so, express it as a linear combination using a, b, and c as the names of the vectors above 14 < Select an answer > v2 = 216
Consider the following vectors: 2 2 2 10 -3 For each of the following vectors, determine whether it is in span (a, b, cj. If so, express...
Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.) S = {(6, -7, 8, 6), (4, 6, -4,1)} (a) u = (18, 43, -32,0) (b) v=(4,1, 75, -10, 13) (c) w=(-4,-14, 15, 15) (d) z= (12, -6, 9, 39)
7. V={[)a620) a vector space! Draw the vector space? Draw the graph and explain why or why not? I. Verify the axiom for polynomial. p(x) = 2t' +31° +1+1 9(x) = 4r +57 +31 + 2 8. p(t)+9(1) € P. 9. p(t)+q(t) = f(t)+p(1) 10. cp(1) EP A subspace of a vector V is a subset H that satisfies what three conditions? 12. Is 0 a subspace of R" 13. Let V, V, E V; show H = span{v. v)...
Please show work
Problem 2. Consider the vectors [1] 1 1 v1 = 1, V2 = -1, V3 = -3 , 04 = , 05 = 6 Let S CR5 be defined by S = span(V1, V2, V3, V4, 05). A. Find a basis for S. What is the dimension of S? B. For each of the vectors V1, V2, V3, V4.05 which is not in the basis, express that vector as linear combination of the basis vectors. C. Consider...
Consider the following vectors. 9 0 6 0 Give the corresponding linear combination. (If an answer does not exist, enter DNE.) 1I Is the vector v a linear combination of the vectors u1 and u? O The vector v is a linear combination of u and u 2 The vector v is not a linear combination of u1 and u2-
Consider the following vectors. 9 0 6 0 Give the corresponding linear combination. (If an answer does not exist, enter...
Consider the following vectors 4 4 For each of the following vectors, determine whether it is in spana, b, c. If so, express it as a linear combination using a, b, and c as the names of the vectors above < Select an answer > 4 14 20 < Select an answer > < Select an answer >
Problem 1: consider the set of vectors in R^3 of the
form:
Material on basis and dimension Problem 1: Consider the set of vectors in R' of the form < a-2b,b-a,5b> Prove that this set is a subspace of R' by showing closure under addition and scalar multiplication Find a basis for the subspace. Is the vector w-8,5,15> in the subspace? If so, express w as a linear combination of the basis vectors for the subspace. Give the dimension of...