MathAlgebraLinear algebraMatrix decomposition

Diagonalization of matrices

Using the diagonalization

Report a typo

We have the matrix: $A= \begin{bmatrix} 3 & 1 & 0 & 0 \\ 0 & 2 & 0 & 0 \\ 0 & 0 & 4 & 1 \\ 0 & 0 & 0 & 5 \\ \end{bmatrix}$ with diagonalization: $D= \begin{bmatrix} 3 & 0 & 0 & 0 \\ 0 & 2 & 0 & 0 \\ 0 & 0 & 4 & 0 \\ 0 & 0 & 0 & 5 \\ \end{bmatrix}$ $P= \begin{bmatrix} 1 & -1 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 1 \\ \end{bmatrix}$ . Calculate the fourth power of $A$ , that is, $A^4$ .

Select one option from the list

\begin{bmatrix} 42 & 0 & 0 & 31 \\ 0 & 91 & 42 & 12 \\ 42 & 3 & 41 & 39 \\ 23 & 4 & 0 & 84 \\ \end{bmatrix}

\begin{bmatrix} 81 & 65 & 0 & 0 \\ 0 & 16 & 0 & 0 \\ 0 & 0 & 256 & 369 \\ 0 & 0 & 0 & 625 \\ \end{bmatrix}

\begin{bmatrix} 0 & 0 & 32 & 17 \\ 13 & -32 & 47 & 0 \\ 0 & 0 & -201 & 89 \\ 0 & -14 & 0 & 83 \\ \end{bmatrix}

\begin{bmatrix} -81 & -4 & 0 & 0 \\ 0 & 2 & 0 & -123 \\ 0 & 0 & 321 & 88 \\ 0 & 0 & 0 & 625 \\ \end{bmatrix}

___

Create a free account to access the full topic