Diagonalization

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The matrix $A = \begin{pmatrix} 3 & 1 \\ -2 & 6 \end{pmatrix}$ is diagonalizable as $A = PDP^{-1}$ . Taking the eigenvalues in increasing order on the diagonal, what is $D$ ?

D = \begin{pmatrix} -4 & 0 \\ 0 & -5 \end{pmatrix}

D = \begin{pmatrix} 5 & 0 \\ 0 & 6 \end{pmatrix}

D = \begin{pmatrix} 5 & 0 \\ 0 & 4 \end{pmatrix}

D = \begin{pmatrix} 4 & 0 \\ 0 & 5 \end{pmatrix}

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The matrix $A = \begin{pmatrix} -10 & 7 \\ -14 & 11 \end{pmatrix}$ is diagonalizable as $A = PDP^{-1}$ . Taking the eigenvalues in increasing order on the diagonal, what is $D$ ?

D = \begin{pmatrix} -3 & 0 \\ 0 & 4 \end{pmatrix}

D = \begin{pmatrix} 4 & 0 \\ 0 & -3 \end{pmatrix}

D = \begin{pmatrix} 3 & 0 \\ 0 & -4 \end{pmatrix}

D = \begin{pmatrix} -2 & 0 \\ 0 & 5 \end{pmatrix}

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The matrix $A = \begin{pmatrix} 2 & 1 \\ -2 & 5 \end{pmatrix}$ is diagonalizable as $A = PDP^{-1}$ . Taking the eigenvalues in increasing order on the diagonal, what is $D$ ?

D = \begin{pmatrix} 4 & 0 \\ 0 & 5 \end{pmatrix}

D = \begin{pmatrix} 4 & 0 \\ 0 & 3 \end{pmatrix}

D = \begin{pmatrix} 3 & 0 \\ 0 & 4 \end{pmatrix}

D = \begin{pmatrix} -3 & 0 \\ 0 & -4 \end{pmatrix}

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Diagonalization

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