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 the statement is true, give a justification. If V₁, V₂, V3 are in R³ and v3 is not a linear combination of V₁, V₂, then {V₁, V₂, V3} is linearly independent. 1: Fill in the blanks below. The statement is Take v₁ and v₂ to be multiples of one vector and take v3 to be not a multiple of that vector. For example, v₁ = 1 V₂= is a linear combination of the other two, the three vectors are linearly V3 Since at least one of the vectors

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.7: Distinguishable Permutations And Combinations
Problem 30E
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true / false
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Please explain why

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 the statement is true, give a justification.
If V₁, V₂, V3 are in R³ and v3 is not a linear combination of V₁, V₂, then {V₁, V2, V3} is linearly independent.
Fill in the blanks below.
The statement is
Take V₁
and v₂ to be multiples of one vector and take v3 to be not a multiple of that vector. For example, v₁
is a linear combination of the other two, the three vectors are linearly
2
-0-0-8
2
1
2
=
=
1
O
Since at least one of the vectors
Transcribed Image Text: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 the statement is true, give a justification. If V₁, V₂, V3 are in R³ and v3 is not a linear combination of V₁, V₂, then {V₁, V2, V3} is linearly independent. Fill in the blanks below. The statement is Take V₁ and v₂ to be multiples of one vector and take v3 to be not a multiple of that vector. For example, v₁ is a linear combination of the other two, the three vectors are linearly 2 -0-0-8 2 1 2 = = 1 O Since at least one of the vectors
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