Mathematics

Mathematics, 19.07.2019 00:30, PlzHelpMeOutKam2693

True or false: if {v1,} is a linearly independent subset of r^n and a is a non-zero scalar, then {w1,} is also a linearly independent set of vectors where w_i=av_i, for i between 1 and k.

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Mathematics, 26.06.2019 22:20, allyssaharrisooy50au

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Mathematics, 12.09.2019 21:30, later

Mark the statement either true (in all cases) or false (for at least one example). if false, construct a specific example to show that the statement is not always true. such an example is called a counterexample to the statement. if the statement is true, give a justification. if v1,…,v4 are in r4 and {v1,v2,v3} is linearly dependent then {v1,v2,v3,v4} is also linearly dependent. select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (a) true. because v3 = 2v1 + v2, v4 must be the zero vector. thus, the set of vectors is linearly dependent. (b) true. the vector v3 is a linear combination of v1 and v2, so at least one of the vectors in the set is a linear combination of the others and set is linearly dependent. (c) true. if c1 =2, c2 = 1, c3 = 1, and c4 = 0, then c1v1 + + c4v4 =0. the set of vectors is linearly dependent. (d) false. if v1 = v2 = v3 = and v4 = [1 2 1 2], then v3 = 2v1 + v2 and {v1, v2, v3, v4} is linearly independent.

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Physics, 26.09.2019 20:00, edfrank6278

The following statement is either true (in all cases) or false (for at least one example). if false, construct a specific example to show that the statement is not always true. such an example is called a counterexample to the statement. if a statement is true, give a justification. if v1 and v2 are in set of real numbers r superscript 4 and v2 is not a scalar multiple of v1, then {v1,v2} is linearly independent. choose the correct answer below. a. the statement is false. the vector v1 could be a scalar multiple of vector v2. b. the statement is false. the vector v1 could be the zero vector. c. the statement is true. a set of vectors is linearly independent if and only if none of the vectors are a scalar multiple of another vector. d. the statement is false. the vector v1 could be equal to the vector v2.

Answers: 2

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