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 V is not a linear combination of V₁, V₂, then {V₁, V₂, V3} is linearly independent. Fill in the blanks below. The statement is + V₂ = 2 2 false/true Take v, and v₂ to be multiples of one vector and take v. to be not a multiple of that vector. For example, V₂ = 0 Since at least one of the vectors is a linear combination of the other two, the three vectors are linearly -deget/Indecent

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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.
alie/tuve
Take v₁ and v₂ to be multiples of one vector and take v. to be not a multiple of that vector. For example,
Fill in the blanks below.
The statement is
-8--8
-
1
=
= 2 V3 = 0 Since at least one of the vectors is a linear combination of the other two, the three vectors are linearly
0
deped /Independ
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. alie/tuve Take v₁ and v₂ to be multiples of one vector and take v. to be not a multiple of that vector. For example, Fill in the blanks below. The statement is -8--8 - 1 = = 2 V3 = 0 Since at least one of the vectors is a linear combination of the other two, the three vectors are linearly 0 deped /Independ
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