Finding S

gabriel

Hey guys, I've been working on my matrix for diagonalization of matrix but am having trouble coming up for my columns of S. Was wondering if anyone could shed some light on this. So far I have

$$ M_1=
\begin{bmatrix}
2 & -3 & -2 \\
1 & -8 & -8\\
-3 & 9 & 9
\end{bmatrix}
M_2=
\begin{bmatrix}
1 & -4 & -3 \\
0 & -9 & -9\\
-4 & 8 & 8
\end{bmatrix}
M_3=
\begin{bmatrix}
0 & -5 & -4 \\
-1 & -10 & -10\\
-5 & 7 & 7
\end{bmatrix}$$

And when I reduce these three matrices, I get
$$
Mr_1=
\begin{bmatrix}
1 & 0 & 0 \\
0 & 1 & 1\\
0 & 0 & 0
\end{bmatrix}
Mr_2=
\begin{bmatrix}
1 & 0 & 0 \\
0 & 1 & 0\\
0 & 0 & 1
\end{bmatrix}
Mr_3=
\begin{bmatrix}
1 & 0 & 0 \\
0 & 1 & 0\\
0 & 0 & 1
\end{bmatrix} $$

I am having difficulty understanding how we come up with $$ s_1, s_2, s_3$$

mark

I'm not sure what's going on here but it looks like you figured out the diagonalization problem.

dan

The columns of S are the eigenvectors. You put them in order that you put the eigenvalues that make up D