Proving Linear Dependence of 3 Vectors with 3 Unknowns

[lo2]

I have these 3 vectors. And I have to prove that they are dependent.

a=(-1,7,-4)

b=(3,5,-6)

a=(15,-1,-12)

I have tried to make 3 equtations with 3 unknows and the solve it. But I just get that the constants should be 0, what they should not be in order to prove they are dependent?

 

[courtrigrad]

So A = \begin{bmatrix}<br /> -1&amp;7&amp;4 \\<br /> <br /> \end{bmatrix}

So B = \begin{bmatrix}<br /> 3&amp;5&amp;-6 \\<br /> <br /> \end{bmatrix}

So C = \begin{bmatrix}<br /> 15&amp;-1&amp;-12 \\<br /> <br /> \end{bmatrix}

For the vectors to be linearly dependent, \left| \begin{array} {ccc} -1 &amp; 7 &amp; 4 \\ 3 &amp; 5&amp; -6 \\ 15 &amp; -1 &amp; -12 \\ \end{array} \right|= 0

 

[Hootenanny]

Alternatively, if you don't like evaluating determinants you could try row reduction to the echelon form (obtaining a final row of zeros would indicate LD).