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
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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