Consider the set of vectors S = {(1, 0, 1),(1, 1, 0),(0, 1, 1)}. (a) Does...

Consider the set of vectors S = {(1, 0, 1),(1, 1, 0),(0, 1, 1)}.

(a) Does the set S span R3?

(b) If possible, write the vector (3, 1, 2) as a linear combination of the vectors in S. If not possible, explain why.

Solutions

Expert Solution

Solution:

(a) Let be arbitary

Consider

(b) Consider,

we have,

Put

milcah answered 1 year ago

Next > < Previous

Related Solutions

Consider the following set of vectors in R6 S={[-9 7 -8 3 0 -5], [1 -7...

Consider the following set of vectors in R6 S={[-9 7 -8 3 0 -5], [1 -7 3 2 -8 -8], [-6 -14 1 9 -23 -29], [11 -21 14 1 -16 -11], [8 16 -8 8 10 1], [17 -7 13 -8 8 18] (a) (2 points) Demonstrate that S is not a basis for R6. (b) (4 points) Let H = Span S. Find a basis for H and determine its dimension. (c) (2 points) Determine whether v= [1,1,1,−1,−1,−1]...

Let S be the set of vectors in R4 S ={(1,1,-1,2),(1,0,1,3),(1,-3,2,2),(0,-2-1,-2)} (a) State whether the vectors...

Let S be the set of vectors in R4 S ={(1,1,-1,2),(1,0,1,3),(1,-3,2,2),(0,-2-1,-2)} (a) State whether the vectors in the set are linearly independent. (b) Find the basis for S. (c) Find the dimension of the column space (rank S). (d) Find the dimension of the null space (nullity S). (e) Find the basis for the null space of S?

Consider the set of vectors {(?,?,?) ∈ ?3???ℎ ?ℎ?? ? − 3? + 5? = 0.}...

Consider the set of vectors {(?,?,?) ∈ ?3???ℎ ?ℎ?? ? − 3? + 5? = 0.} Does this set of vectors form a sub-space of ?3?

Consider the following vectors: →a = 5 −1 3 3 →b = 5 0 1 0...

Consider the following vectors: →a = 5 −1 3 3 →b = 5 0 1 0 →c = −10 3 −3 −7 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 = 5 −3 2 7 < Select an answer > →v2 = 2 7 6 −7 < Select an answer > →v3 =...

3. In R4 , does the set {(1, 1, 1, 0,(1, 0, 0, 0),(0, 1, 0,...

3. In R4 , does the set {(1, 1, 1, 0,(1, 0, 0, 0),(0, 1, 0, 0),(0, 0, 1, 1)}, span R4? In other words, can you write down any vector (a, b, c, d) ∈ R4 as a linear combination of vectors in the given set ? Is the above set of vectors linearly independent ? 4. In the vector space P2 of polynomials of degree ≤ 2, find explicitly a polynomial p(x) which is not in the span...

What does it means for a set of vectors a1; a2; : : : ; ;...

What does it means for a set of vectors a1; a2; : : : ; ; an to be linearly independent? What is the span of the set? This question is about linear algebra

Prove the follwing statements Suppose that S is a linearly independent set of vectors in the...

Prove the follwing statements Suppose that S is a linearly independent set of vectors in the vector space V and let w be a vector of V that is not in S. Then the set obtained from S by adding w to S is linearly independent in V. If U is a subspace of a vector space V and dim(U)=dim(V), then U=V.

1: Let X be the set of all ordered triples of 0’s and 1’s. Show that...

1: Let X be the set of all ordered triples of 0’s and 1’s. Show that X consists of 8 elements and that a metric d on X can be defined by ∀x,y ∈ X: d(x,y) := Number of places where x and y have different entries. 2: Show that the non-negativity of a metric can be deduced from only Axioms (M2), (M3), and (M4). 3: Let (X,d) be a metric space. Show that another metric D on X can...

Let A be some m*n matrix. Consider the set S = {z : Az = 0}....

Let A be some m*n matrix. Consider the set S = {z : Az = 0}. First show that this is a vector space. Now show that n = p+q where p = rank(A) and q = dim(S). Here is how to do it. Let the vectors x1, . . . , xp be such that Ax1, . . . ,Axp form a basis of the column space of A (thus each x can be chosen to be some unit...

Consider the set of integer numbers from 0 to 9, that is {0, 1, 2, 3,...

Consider the set of integer numbers from 0 to 9, that is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. Bob wishes to use these numbers to create a 7-digit password to secure his new laptop. Note that each number can appear in any position (for example, 0 can be the first number in the password). (a) Find the number of 7-digit passwords that are possible. (b) Find the number of 7-digit passwords with distinct digits. (c) Find...

Subjects