i) A set of 4 6-tuples (“sextuplets”) is linearly independent: (always), (never), (sometimes). ii) A set...

i) A set of 4 6-tuples (“sextuplets”) is linearly independent: (always), (never), (sometimes). ii) A set of 6 4-tuples (“quadruplets”) is linearly independent: (always), (never), (sometimes). iii) A set of 4 equations with 6 unknown variables which is consistent has a unique solution: (always), (never), (sometimes). iv) A set of 4 equations with 6 unknown variables is inconsistent: (always), (never), (sometimes) v) A set of homogeneous equations is inconsistent: (always), (never), (sometimes) vi) The solution to a set of homogeneous equations is unique: (always), (never), (sometimes)

Expert Solution

Colby Messinger answered 2 years ago

For each of the following statements, determine if the statement is always, sometimes, or never true....

For each of the following statements, determine if the statement is always, sometimes, or never true. Justify your statement with a proof. Hint: To prove that something isn’t always true, it is sufficient to provide a counterexample. (a) If L is an unrecognizable language, then L is (always/sometimes/never) undecidable. (b) If L is a recognizable language then L COMPLEMENT is (always/sometimes/never) recognizable.

Read the following statements and decide if they are true sometimes, always or never. Be sure...

Read the following statements and decide if they are true sometimes, always or never. Be sure to give a reason for each statement or use an example and the reason why it shows the statement is false. You can download this document in the module one section Fractions and attach it if you prefer. All fractions are less than one Improper fractions are greater than or equal to one Proper fractions are less than one Fractions are always part of...

Determine whether each set of vectors is linearly dependent or linearly independent. a) (1,1,0,1), (1,0,1,1), (0,1,1,1)...

Determine whether each set of vectors is linearly dependent or linearly independent. a) (1,1,0,1), (1,0,1,1), (0,1,1,1) b) (1,0,1,0), (0,1,0,1), (1,-1,1,-1), (1,-1,0,0)

Determine whether the members of the given set of vectors are linearly independent. If they are...

Determine whether the members of the given set of vectors are linearly independent. If they are linearly dependent, find a linear relation among them of the form c1x(1) + c2x(2) + c3x(3) = 0. (Give c1, c2, and c3 as real numbers. If the vectors are linearly independent, enter INDEPENDENT.) x(1) = 9 1 0 , x(2) = 0 1 0 , x(3) = −1 9 0

Statement evaluation. Indicate whether each of the following statements is (i) always true, (ii) sometimes true,...

Statement evaluation. Indicate whether each of the following statements is (i) always true, (ii) sometimes true, or (iii) never true. For those that are (ii) sometimes true; explain when the statement is true. a. All necessary XBRL tags were developed by the XBRL Consortium. b. Companies must use software to prepare XBRL instance documents. c. Companies that do business in a single country do not need XBRL. d. DiversifiedorganizationsshoulduseXBRL. e. General ledger software can create XBRL tags. f. OrganizationsthatadoptXBRLmustcreatetheirownnamespace. g....

A basis of a vector space V is a maximal linearly independent set of vectors in...

A basis of a vector space V is a maximal linearly independent set of vectors in V . Similarly, one can view it as a minimal spanning set of vectors in V . Prove that any set S ⊆ V spanning a finite-dimensional vector space V contains a basis of V .

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.

Which of the following sets of functions are linearly independent on the interval (−∞, ∞)? (i) ...

Which of the following sets of functions are linearly independent on the interval (−∞, ∞)? (i) f1(x) = x, f2(x) = 6x, f3(x) = x2 + 3 (ii) f1(x) = 2e2x, f2(x) = 4e4x, f3(x) = 8e8x (iii) f1(x) = 4sin2x, f2(x) = 10cos 2x, f3(x) = x (A) (ii) only (B) (iii) only (C) (i) and (iii) only (D) (ii) and (iii) only (E) all of them (F) (i) and (ii) only (G) (i) only (H) none of them

Are health care facilities in USA natural monopolies a) never, b) sometimes, c) always? If a),...

Are health care facilities in USA natural monopolies a) never, b) sometimes, c) always? If a), should “duplication of services” be illegal? If b), give one example of each case. If c), should the price of healthcare be regulated, like the price of retail electricity?

1. Determine each of the following set of vectors is linearly independent or dependent. (a) S1...

1. Determine each of the following set of vectors is linearly independent or dependent. (a) S1 = {(1, 2, 3),(4, 5, 6),(6, 9, 12)}. (b) S2 = {(1, 2, 3, 4),(5, 6, 7, 8),(3, 2, 1, 0)}. (c) S3 = {(1, 2, 3, 4),(5, 6, 7, 8),(9, 10, 11, 12)}

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