- (a)
- The vector \(\vec {v}_1=\begin{bmatrix}-4\\1\\-3\end{bmatrix}\) is an eigenvector of \(A\) because \(A\vec {v}_1= \lambda _1 \vec {v}_1\) where \(\lambda _1 = \) -3 -1 2
- (b)
- The vector \(\vec {v}_2=\begin{bmatrix}8\\-2\\7\end{bmatrix}\) is an eigenvector of \(A\) because \(A\vec {v}_2= \lambda _2 \vec {v}_2\) where \(\lambda _2 = \) -3 -1 2
- (c)
- The vector \(\vec {v}_3=\begin{bmatrix}4\\-1\\4\end{bmatrix}\) is an eigenvector of \(A\) because \(A\vec {v}_3= \lambda _3 \vec {v}_3\) where \(\lambda _3 = \) -3 -1 2
- (d)
- Since the Power Method converges to the dominant eigenvector, it can be used
to approximate which eigenvector of \(A\)? \(\vec {v}_1\) \(\vec {v}_2\) \(\vec {v}_3\)
.