I have to find k such that:
$v=(k-5,12-k,7)$ and $w=(k+1,k-6,4-k)$ are linearly dependent.
I have found that $A=\begin{bmatrix}k-5 &12-k &7\\ k+1 &k-6 &4-k
\end{bmatrix}$ has rank always equal to 2. (I have verified that: the three minors of order 2 are invertible)
Then I have to conclude that they are surely linearly independent?
I am not sure of this since the excercise ask to find k.
2026-04-01 04:20:55.1775017255
Find k such that two vectors are linearly dependent
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