If A=beginbmatrix 7 & 2 -4 & 1 endbmatrix, find a formula for An, wher | Mathematics II 2078

Mathematics II20785 marksNumerical: matrix power formulaDiagonalization

If $A=\begin{bmatrix} 7 & 2 \\ -4 & 1 \end{bmatrix}$ , find a formula for $A^n$ , where $A = PDP^{-1}$ , $P=\begin{bmatrix} 1 & 1 \\ -1 & -2 \end{bmatrix}$ and $D=\begin{bmatrix} 5 & 0 \\ 0 & 3 \end{bmatrix}$ [5]

If $A=\begin{bmatrix} 7 & 2 \ -4 & 1 \end{bmatrix}$, find a formula for $A^n$, where $A = PDP^{-1}$, $P=\begin{bmatrix} 1 & 1 \ -1 & -2 \end{bmatrix}$ and $D=\begin{bmatrix} 5 & 0 \ 0 & 3 \end{bmatrix}$ [5]

Given data: $A = \begin{bmatrix} 7 & 2 \\ -4 & 1 \end{bmatrix}, \quad P = \begin{bmatrix} 1 & 1 \\ -1 & -2 \end{bmatrix}, \quad D = \begin{bmatrix} 5 & 0 \\ 0 & 3 \end{bmatrix}$ Relation: $A = PDP^{-1}$ . Required: formula for $A^n$ . Key fact: $A^n = (PDP^{-1})^n = PD^nP^{-1}$ . Find $P^{-1}$ : $$...

Given data: $$A = \begin{bmatrix} 7 & 2 \ -4 & 1 \end{bmatrix}, \quad P = \begin{bmatrix} 1 & 1 \ -1 & -2 \end{bmatrix}, \quad D = \begin{bmatrix} 5 & 0 \ 0 & 3 \end{bmatrix}$$ Relation: $A = PDP^{-1}$. Required: formula for $A^n$. Key fact: $A^n = (PDP^{-1})^n = PD^nP^{-1}$. Find $P^{-1}$: $$...

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If A=beginbmatrix 7 & 2 -4 & 1 endbmatrix, find a formula for An, where A = PDP-1, P=beginbmatrix 1 & 1 -1 & -2 endbmatrix and D=beginbmatrix 5 & 0 0 & 3 endbmatrix