Question

(1 pt) The eigenvalues of a matrix $A$ are $\lambda_1 = 2$, with corresponding eigenvector $\vec{v_1} = \begin{bmatrix} -1 \\ 3 \end{bmatrix}$, and $\lambda_2 = 1$ with corresponding eigenvector $\vec{v_2} = \begin{bmatrix} -2 \\ 5 \end{bmatrix}$ Find a diagonal matrix $D$ that is similar to $A$. $D = \begin{bmatrix} \\ \\ \end{bmatrix}$ Find an invertible matrix $P$ such that $P^{-1}AP = D$. $P = \begin{bmatrix} \\ \\ \end{bmatrix}$ Find $A$ itself. $A = \begin{bmatrix} \\ \\ \end{bmatrix}$ Finally, find $A^5$ $A^5 = \begin{bmatrix} \\ \\ \end{bmatrix}$

          (1 pt) The eigenvalues of a matrix $A$ are $\lambda_1 = 2$, with corresponding eigenvector $\vec{v_1} = \begin{bmatrix} -1 \\ 3 \end{bmatrix}$, and $\lambda_2 = 1$ with corresponding eigenvector $\vec{v_2} = \begin{bmatrix} -2 \\ 5 \end{bmatrix}$
Find a diagonal matrix $D$ that is similar to $A$.
$D = \begin{bmatrix} \\ \\ \end{bmatrix}$
Find an invertible matrix $P$ such that $P^{-1}AP = D$.
$P = \begin{bmatrix} \\ \\ \end{bmatrix}$
Find $A$ itself.
$A = \begin{bmatrix} \\ \\ \end{bmatrix}$
Finally, find $A^5$
$A^5 = \begin{bmatrix} \\ \\ \end{bmatrix}$

(1 pt) The eigenvalues of a matrix A are λ1 = 2, with corresponding eigenvector v⃗1⃗ =
< b m a t r i x >, and λ2 = 1 with corresponding eigenvector v⃗2⃗ =
< b m a t r i x >
Find a diagonal matrix D that is similar to A.
D =
< b m a t r i x >
Find an invertible matrix P such that P^-1AP = D.
P =
< b m a t r i x >
Find A itself.
A =
< b m a t r i x >
Finally, find A^5
A^5 =
< b m a t r i x >

Added by Claudia B.

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