Determine if the set is a basis for R3. Justify your answer. 3 4 - 2 Is the given set a basis for R3? O A. No, because these three vectors form the columns of a 3x3 matrix that is not invertible. By the invertible matrix theorem, the following statements are equivalent: A is an invertible matrix, the columns of A form a linearly independent set, and the columns of A span R". O B. No, because these three vectors form the columns of an invertible 3x3 matrix. By the invertible matrix theorem, the following statements are equivalent: A is a singular matrix, the columns of A form a linearly independent set, and the columns of A span R". Oc. Yes, because these three vectors form the columns of a 3x3 matrix that is not invertible. By the invertible matrix theorem, the following statements are equivalent: A is a singular matrix, the columns of A form a linearly independent set, and the columns of A span R". O D. Yes, because these three vectors form the columns of an invertible 3x3 matrix. By the invertible matrix theorem, the following statements are equivalent: A is an invertible matrix, the columns of A form a linearly independent set, and the columns of A span R".

Q: 1) -141, Vī, -8.5 , vZ , 1000

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: 2.) Create two sets, A and B such that An B = 0 and A UB= (1,2,3,4).

A:

Q: In how many ways can they sit so that the dinner may NOT end in a disaster (i.e. how many ways can…

A:

Q: In Muscat city, there are two types of services at a gas station. The gas station has a single…

A: Given Information: A\B 0 1 2 PA(A) 0 0.14 0.02 0.09 0.25 1 0.05 0.29 0.05 0.39 2 0.10 0.13…

Q: Let a1 = [-2  h], and a2 = [10  -20] The set {a1,a2} will span R3 unless h

A:

Q: Select the set that is equivalent to (Cn B) UA. (Cn B)UA (CUB) UA (CnB) nA (CUB) NA

A:

Q: Say True or False and justify your answer. P(A∪B)⊆P(A)∪P(B)

A:

Q: Give an example of sets A and B for which |A U B| = |A|+|B|.

A:

Q: The set {[1 -1 3], [2 3 -2], [3 2 1], [0 0 0]} spans صواب İhi

A:

Q: If U is the set of all multiples of 3 less than 20, and M={3,12,18}, find Mc (the complement of M).…

A:

Q: Express the set in roster form. B = (x | XEN and x is a multiple of 7)

A: For given set B we have to write it in roster form.

Q: If P = {1, 2}, form the set P × P × P.

A:

Q: Prove or disprove: For all sets A, B, we must have 24A2(AAB) = 2B.

A: Given, 2A∆2A∆B

Q: Use any method you choose to shc are sets.

A:

Q: 4. Let A and B be sets. (a) If A and B are subsets of the same universal set U (so A × B is a subset…

A: The definition of complement is given at the end of proof

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

A:

Q: State whether each of the following statement is true or false. Justify your answer.(i) { 2, 3, 4, 5…

A:

Q: What is the domain of the set g= {(2, 1), (3, 5), (4, 7), (5, 9)}

A: GIVEN-  set g is given g={ (2, 1) , (3, 5), (4, 7), (5, 9) }  TO FIND -  DOMAIN OF set g  CONCEPT-…

Q: Answer the following True or False. (a) {1,2,3} is a subset of {3,2, 1, 4}. (b) {3,2, 1, 4} is a…

A:

Q: Activity: (PIUVRue anouiCI 31CCt A.) Complete the table below. Illustrates the union (U) and…

A: The operator "∩" denotes the intersection of sets. For example: A∩B denotes the set which contains…

Q: Assume that A, B, C and D are sets. Verify that (A x B) U (C x D) ≤ (AUC) x (BUD).

A:

Q: If={1,2,3,4,5) and = (0,0, (1), (2,3), (4,5), (1,2,3), (1,4,5), (2,3,4,5)} then If Q=set of positive…

A:

Q: Find the intersection of the sets. {a, b, c, d}∩∅

A: Given sets are {a, b, c, d} and an empty set ϕ

Q: Give an example of four sets A, B, C and D such that (AUC) x (BUD) ≤ (A x B) U (C x D).

A: The set A is a subset of B if every element of A is in B

Q: Determine which sets in Exercises 1-8 are bases for R³. Of the sets that are not bases, determine…

A:

Q: Express the set using the roster method. (x| xEN and x> 9) Choose the correct answer below. O A.…

A:

Q: (2b) Let A and B be sets. Prove that A – B is disjoint from A n BC LA O BE

A: The set A∩B is defined as A∩B=x|x∈A and x∈B The set A-B is defined as A-B=x|x∈A and x∉B Two sets are…

Q: Let A, B and C be sets. Use the algebra of sets to verify each statement. Suppose, A AB -(A-B)u…

A:

Q: How do i approach the following question?  Let A and B be sets. Prove that A ∪ B = A ∩ B if and…

A:

Q: Show that if A and B are sets, then P(A) u P(B) c P(A u B), where P(A) denotes the power set of A

A:

Q: 4.) If the Cartesian product of A x B is {(1, 1), (1, 2), (3, 1), (3, 2), (5, 1), (5, 2)), what are…

A: Topic- Cartesian products of sets we are given, A×B={(1,1),(1,2),(3,1),(3,2)(5,1),(5,2)}if…

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.