Stats Solutions

[See Solution] Define A, I, O and X as follows:

Question: Define \(\mathbf{A}, \mathbf{I}, \mathbf{O}\) and \(\mathbf{X}\) as follows:

\[\mathbf{A}=\left(\begin{array}{lll} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array}\right) \quad \mathbf{I}=\left(\begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right) \quad \mathbf{X}=\left(\begin{array}{l} 0 \\ 0 \\ 0 \end{array}\right) \quad \mathbf{X}=\left(\begin{array}{l} x_{1} \\ x_{2} \\ x_{3} \end{array}\right)\]

The equation \(\mathbf{A X}=\lambda \mathbf{X}\) can be rewritten as

\[(\mathbf{A}-\lambda \mathbf{I}) \mathbf{X}=\mathbf{O}\]

Find all solutions \(X\) for each of the following cases:

\[\lambda=0 \quad \lambda=1 \quad \lambda=-1\]

Price: $2.99
Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document


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