(a) Let V be as defined below. 221 -13 -8 4 V = 6 -13 5 -9 {v1,v2,v3,v4}={ { 14, -8, -4, -4, 4}, { -2, 0, { 22, -8, -13, -9, 9}, {-13, 4, 6, 4, 0}, 5, 3, -7}} Is v a linearly independent set? Explain.

Q: Determine whether the given set is linearly dependent or linearly independent: S =

A:

Q: QUESTION 7 Given binary relation, R = {(0, 0),(1, 1),(2,2) } is is defined on set on A = {0, 1, 2,…

A:

Q: Q2. Let X = {a, b, c, d, m, n}, 7 = {6, X, {c}. {m,n}, {a, b, c, d}, {c, m, n}}. and Y- (b,c, m) C…

A:

Q: Set roster notation of U={r € Z l -2<r<2

A: we have given the set U = {r∈Z,  -2&lt;r&lt;2} we have to write the set roster notation of U The set…

Q: Let A be a set and let ƒ : A → B be a surjective function. Prove that there exists a subset CCA such…

A: Given: A be a set and f:A→B is a surjective function. To prove: There exists a subset C⊂A such that…

Q: O (A) O (B) O (c) O (D) O (E) If the set {(1, 2, 1), (0, 1, 1), (1, -2, A)} is linearly independent,…

A: We have the set 1,2,1, 0,1,1, 1,-2, λ A set is linearly independent if the determinant of the matrix…

Q: pdf. Every nonempty proper subset of Ris either open or closed.

A: False

Q: Show that the sets [0,1] and (0, 1) are equinumerous 7.

A:

Q: Which of the following sets is a function? * {(a, a)b,b)\a,c)} {(a,b){b,cXc,a} Option 2 О Оption 4…

A: We have to identify which of the following set is a function.

Q: { O True O False The set 5 1 4 -4 1 -3 5 is linearly independent.

A:

Q: R relation for A = {a, b, c, d, e, f} partially ordered set and subset B = {b, c, d} Let R = {(b,…

A: Given data: R=b,a,c,d,d,b,e,c,f,d,e,d,f,c which is relation for A=a,b,c,d,e,f partially ordered set…

Q: See the image below. What is the mapping rule that represents the dilation of preimage B to produce…

A:

Q: QUESTION 9 Which functions on (1, 2, 3, 4) × {a, b, c) is NOT onto? O {(1, c), (2, a), (3, a), (4,…

A: Identity function

Q: Create a flow proof for each of the following results. In your flow proof, each step gets its own…

A: Prof:- we know that a⊆a∪b⇒p(a)⊆p(a∪b) ⋯(i) b⊆a∪b ⇒p(b)⊆p(a∪b) ⋯(ii)from (i) and (ii),we…

Q: Determine whether the set S is linearly independent or linearly dependent. S = {(2, 6, 1), (3, -1,…

A: When two vectors are linearly dependent one vector can be written in scalar multiple of other.

Q: Question Show. is Banach space

A:

Q: Let U {1,2,..., 100}, and let A consist of 15 unknown numbers taken ran- %3D domly from U. Let B…

A:

Q: ​Claim: A minority of adults would erase all of their personal information online if they could. A…

A: Here we want to express claim in symbolic form.

Q: Determine whether the given set is linearly independent.

A: We will check that given set is linearly independent or not using definition of linear independency.…

Q: a set A = {1,2, 3, 4} of numbers and a set B = {a, b, c, d} of letters. {(1, d), (2, d) , (3, a) ,…

A:

Q: What is Partial Ordering Relation and give an example.   What is Equivalence Relation and give an…

A: See the attachment

Q: Which of the following sets is linearly independent? * the above set None of these [2 41 the above…

A: All the sets are linearly dependent as shown in step 2 and hence None of these.

Q: Let R = Zg, and let N = R³. Determine whether or not X = {(4, 5, 4), (4, 5, 2), (2, 2, 3)} is a free…

A: It is given that,  R = ℤ8  and  N = R3. We have to determine that whether the set,  X = 4, 5, 4, 4,…

Q: |Given the relation R= {(1,1), (2, 4), (3, 1), (4, 1), (5,2)} on the set A= {1,2,3,4,5), find the…

A: We know: Symmetric closure of a relation R, △, is obtained by adding (b, a) to R for each (a, b) ∈ R…

Q: 18. Let X be a set. Define a relation R on P(X) by look ARB AnB=0 for A, BE P(X). Determine whether…

A: Check the relation

Q: 1.10 For each map, give the chain of range spaces and the chain of null spaces, and the generalized…

A: For each map, we will be giving the chain of range spaces and the chain of null spaces, and the…

Q: what is the closed neighborhood ? And give examples

A:

Q: Which of the following sets is linearly independent? * T2 21 3. 81 3 the above set O the above set…

A: For a 2×2 matrix abcd, if detabcd=0, then matrix is linearly dependent, otherwise linearly…

Q: df. Every nonempty proper subset of R is either open or closed.

A: False

Q: Let A = {1, 2, 3, 4). Define a relation R on A: R = {(1, 2), (1, 3), (2, 2), (2, 3), (3, 4), (4,3)}…

A: Since you have posted a multi subparts question according to guidelines I will solve first…

Q: Which of the following sets spans R? O (3,0,2).(5,1,0),(0,-1,1)} O (-3,0,2),(0,0,.0)} (-3,0,2)) None…

A: To finds sets that spans R3

Q: Examples. Justify your answers briefly. (b) Give an example of a closed subset of R that is not…

A:

Q: It is the selection of objects from a set.

A: This is the problem of combinatorial. finite math, counting.

Q: 1. Consider the relationR =…

A: In mathematics, the reflexive closure of a binary relation R on a set X is the smallest reflexive…

Q: Explain why the set 3 0 3 {}]][ []} 3 3 is a spanning set for R³ but not a linearly independent set.…

A:

Q: a set A = {1,2, 3, 4} of numbers and a set C = {a, b, c, d, e} of letters. {(1, a), (2, b) , (3, c),…

A: Here use definition of mapping And   onto and one to one function

Q: b. Which sets are functions?• (1, 2) (2, 3) (3, 4) Yes/No If no, why• (1, 2), (2, 3) (2, 5) Yes/No…

A: We have given,

Q: 3. Determine if the set Q n (0,1) is open, closed or neither. What is the boundary of the set? Also…

A: 1. Q ∩ (0,1) is neither open nor closed. 2. For the set Q ∩ (0,1), the boundary includes the points…

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.