Writing a Linear Combination In Exercises 55 and 56, the zero vector 0 = (0, 0, 0) can
Chapter 4, Problem 56(choose chapter or problem)
In Exercises 55 and 56, the zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors \(v_{1}, v_{2}\), and \(v_{3}\) because \(0=0 v_{1}+0 v_{2}+0 v_{3}\). This is the trivial solution. Find a nontrivial way of writing 0 as a linear combination of the three vectors, if possible.
\(\mathbf{v}_{1}=(1,0,1), \quad \mathbf{v}_{2}=(-1,1,2), \quad \mathbf{v}_{3}=(0,1,3)\)
Text Transcription:
v_1, v_2
V_3
0=0v_1 +0v_2 +0v_3
mathbf v_1 =(1,0,1), mathbf v_2 =(-1,1,2), mathbf v_3 =(0,1,3
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