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\(\displaystyle r1=2a-3b+c\)

\(\displaystyle r2=3a-5b+2c\)

\(\displaystyle r3=4a-5b+c\)

where \(\displaystyle a, b, c\) are non-zero and non coplannar vectors

How to prove that \(\displaystyle r1, r2 , r3\) are linearly dependent?

I have moved with \(\displaystyle c1*r1+c2*r2+c3*r3=0\)

but confused how to show that at leat one of \(\displaystyle c1, c2, c3\) is non-zero. We only have the information \(\displaystyle a,b,c \neq 0\) and \(\displaystyle [a b c]\neq 0\)