- #1
Nathew
Homework Statement
Determine all values of the constant k for which the given set of vectors is linearly independent in [itex]\mathbb R^4[/itex].
{(1, 1, 0, −1), (1, k, 1, 1), (4, 1, k, 1), (−1, 1, 1, k)}
Homework Equations
The Attempt at a Solution
So far I set up a coefficient matrix
[tex]
\begin{pmatrix}
1 & 1 & 4 & -1 \\
1 & k & 1 & 1 \\
0 & 1 & k & 1 \\
-1 & 1 & 1 & k
\end{pmatrix}
[/tex]
And tried converting it to REF
[tex]
\begin{pmatrix}
1 & 1 & 4 & -1 \\
0 & 1 & k & 1 \\
0 & 0 & (-k^2+k-3) & (3-k) \\
0 & 0 & (5-2k) & (k-3)
\end{pmatrix}
[/tex]
I'm not sure if I should keep going trying to reduce this to REF to see which values of k will not work, but it just seems too messy.
Am I approaching this the wrong way?