- #1
TranscendArcu
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Homework Statement
My instructor wants me to only solve for the case m=2.
The Attempt at a Solution
So I thought I should discover what T does to the standard basis for matrices of size 2x2:
[itex]T \left| \begin{array}{cc}
1 &0 \\
0&0 \end{array} \right| = \left| \begin{array}{cc}
1 &0 \\
0&0 \end{array} \right|[/itex]
[itex]T \left| \begin{array}{cc}
0 &1 \\
0&0 \end{array} \right| =\left| \begin{array}{cc}
0 &0 \\
1&0 \end{array} \right|[/itex]
[itex]T \left| \begin{array}{cc}
0 &0 \\
1&0 \end{array} \right| =\left| \begin{array}{cc}
0 &1 \\
0&0 \end{array} \right|[/itex]
[itex]T \left| \begin{array}{cc}
0 &0 \\
0&1 \end{array} \right| =\left| \begin{array}{cc}
0 &0 \\
0&1 \end{array} \right|[/itex]
At this point do I have to create a matrix consisting of these transformed matrices in order to find [itex]Δ_T (t) = det(M - tI)[/itex]? I'm kind of confused about my next step.