Al P. answered • 03/12/20

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Let:

**a **= **v **+ **w **= [ a_{1 }a_{2} ... a_{n }]

**b **= **v **+ **x **=** **[ b_{1} b_{2} ... b_{n }]

**c **= **w** - **x **= [c_{1 } c_{2 }... c_{n} ]

and note that a_{1} = v_{1}+w_{1, }b_{1} = v_{1}+x_{1}, c_{1} = w_{1}-x_{1}, etc. ...

Then

a_{1} - b_{1} = (v_{1}+w_{1})-(v_{1}+x_{1}) = (w_{1}-x_{1}) = c_{1}

a_{2 }- b_{2} = (v_{2}+w_{2})-(v_{2}+x_{2}) = (w_{2}-x_{2}) = c_{2}

...

a_{n }- b_{n} = (v_{n}+w_{n})-(v_{n}+x_{n}) = (w_{n}-x_{n}) = c_{n}

This shows that the three vectors {**a,b,c**} are linearly dependent.