Question

let V1=U1-xU3, V2=U2, V3=xU1+U3, prove that the vectors are linearly independent at each point in R3

Answer 1

Wait, so \(\vec{v}=\langle v_1,v_2,v_3\rangle\) and \(\vec{u}=\langle u_1,u_2,u_3\rangle\), and these satisfy
\[\begin{cases}
v_1=u_1-xu_3\\v_2=u_2\\v_3=xu_1+u_3
\end{cases}\]
What is \(x\)? Is it a scalar constant?