Question

Problem 2. Consider the following matrix $A$ and vector $v$ $\begin{bmatrix} -1 & 2 & 0 \ -2 & 4 & 1 \ 4 & -7 & -2 \end{bmatrix}$, $v = \begin{bmatrix} 1+i \ 1 \ -2+i \end{bmatrix}$. (a) Prove that $v$ is an eigenvector of $A$. (b) Find an invertible real matrix $P$ and real numbers $a$, $b$, $c$ such that $P^{-1}AP = \begin{bmatrix} a & 0 & 0 \ 0 & b & -c \ 0 & c & b \end{bmatrix}$. (c) Based on item (b) provide an explanation of the action of the matrix $A$ similar to the explanation in the book on page 301. (d) Based on item (c) state what is $A^4$. Explain your reasoning. No calculations are needed here.

          Problem 2. Consider the following matrix $A$ and vector $v$
$\begin{bmatrix} -1 & 2 & 0 \ -2 & 4 & 1 \ 4 & -7 & -2 \end{bmatrix}$, $v = \begin{bmatrix} 1+i \ 1 \ -2+i \end{bmatrix}$.
(a) Prove that $v$ is an eigenvector of $A$.
(b) Find an invertible real matrix $P$ and real numbers $a$, $b$, $c$ such that $P^{-1}AP = \begin{bmatrix} a & 0 & 0 \ 0 & b & -c \ 0 & c & b \end{bmatrix}$.
(c) Based on item (b) provide an explanation of the action of the matrix $A$ similar to the explanation in the
book on page 301.
(d) Based on item (c) state what is $A^4$. Explain your reasoning. No calculations are needed here.

Problem 2. Consider the following matrix A and vector v
< b m a t r i x >, v =
< b m a t r i x >.
(a) Prove that v is an eigenvector of A.
(b) Find an invertible real matrix P and real numbers a, b, c such that P^-1AP =
< b m a t r i x >.
(c) Based on item (b) provide an explanation of the action of the matrix A similar to the explanation in the
book on page 301.
(d) Based on item (c) state what is A^4. Explain your reasoning. No calculations are needed here.

Added by Alan B.

Question

Please give Ace some feedback