Math Problem Statement

Consider the set of three vectors S={(1,2,−1),(3,1,0),(−1,2,c)}S={(1,2,−1),(3,1,0),(−1,2,c)} in R3R3 with usual addition and scalar multiplication. For which value of cc will the above set SS be linearly dependent?

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Vector Spaces
Linear Dependence

Formulas

λ1(1, 2, -1) + λ2(3, 1, 0) + λ3(-1, 2, c) = (0, 0, 0)
λ1 + 3λ2 - λ3 = 0
2λ1 + λ2 + 2λ3 = 0
-λ1 + cλ3 = 0

Theorems

Linear Dependence Theorem
System of Linear Equations

Suitable Grade Level

Undergraduate Level (Linear Algebra Course)