Let $v_1=(1,0,1)$, $v_2=(0,1,1)$ and $b=(2,3,5)$. Solving $c_1v_1+c_2v_2=b$ gives $c_1=2$ from the first coordinate and $c_2=3$ from the second. The third coordinate checks $2+3=5$. Thus $b=2v_1+3v_2$. A target $(2,3,6)$ would not lie in their span.
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