Linear Independent -prove

[ku1005]

"Let a, be non-zero, non-paralell vectors in R^3. Prove that the set



is linearly independent.

[Hint: You may use the fact that every pair of non-zero non-paralell vecotrs is linearly inependent.]"

In my head I know that this is true, im just not sure how to go about setting out a proof for this question, and it was worth 10 marks on a previous exam I am viewing (for study purposes).Just wondering if anyone could just give me an outline of the answer.cheers

 

[Deleted member 4993]

What is the mathematical definition of - linearly independent

 

[pka]

From the given we know that \(\displaystyle \L a \times b\) is non-zero.
Both \(\displaystyle \L a\,\& \,b\) are perpendicular to \(\displaystyle \L {a \times b}\), so \(\displaystyle \L \alpha a + \beta b\) for scalars \(\displaystyle \L \alpha ,\beta\) is also perpendicular to \(\displaystyle \L {a \times b}\).