- #1
Dustinsfl
- 2,281
- 5
[tex]\begin{bmatrix}
1 & 1 & 0\\
1 & 1 & 0\\
0 & 0 & \alpha
\end{bmatrix}[/tex] and [itex]det(A-\lambda I)=\lambda(\alpha-\lambda)(\lambda-2)=0[/itex]
Therefore, [itex]\lambda_1=0[/itex], [itex]\lambda_2=\alpha[/itex], and [itex]\lambda_3=2[/itex].
In order to make this matrix defective, I need to make the left two column vectors dependent[tex]\begin{bmatrix}
1-\alpha & 1 & 0\\
1 & 1-\alpha & 0\\
0 & 0 & 0
\end{bmatrix}[/tex].
Is there an easy way to find or determine if this can be done for a given matrix?
1 & 1 & 0\\
1 & 1 & 0\\
0 & 0 & \alpha
\end{bmatrix}[/tex] and [itex]det(A-\lambda I)=\lambda(\alpha-\lambda)(\lambda-2)=0[/itex]
Therefore, [itex]\lambda_1=0[/itex], [itex]\lambda_2=\alpha[/itex], and [itex]\lambda_3=2[/itex].
In order to make this matrix defective, I need to make the left two column vectors dependent[tex]\begin{bmatrix}
1-\alpha & 1 & 0\\
1 & 1-\alpha & 0\\
0 & 0 & 0
\end{bmatrix}[/tex].
Is there an easy way to find or determine if this can be done for a given matrix?