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(1) Determine whether the given matrices are diagonalizable or not. If so, then find its diagonalization (it means to find the diagonal matrix D that it is similar to, as well as the change of basis matrix P). (a) A = egin{pmatrix} 2 & -1 \ -1 & 2 end{pmatrix} (b) A = egin{pmatrix} -3 & 2 \ -2 & 1 end{pmatrix} (c) A = egin{pmatrix} 3 & -2 & -4 \ 8 & -7 & -16 \ -3 & 3 & 7 end{pmatrix} (d) A = egin{pmatrix} 3 & -1 & -1 \ -12 & 0 & 5 \ 4 & -2 & -1 end{pmatrix}

          (1) Determine whether the given matrices are diagonalizable or not. If so, then find its diagonalization (it means to find the diagonal matrix D that it is similar to, as well as the change of basis matrix P).
(a) A = egin{pmatrix} 2 & -1 \ -1 & 2 end{pmatrix}
(b) A = egin{pmatrix} -3 & 2 \ -2 & 1 end{pmatrix}
(c) A = egin{pmatrix} 3 & -2 & -4 \ 8 & -7 & -16 \ -3 & 3 & 7 end{pmatrix}
(d) A = egin{pmatrix} 3 & -1 & -1 \ -12 & 0 & 5 \ 4 & -2 & -1 end{pmatrix}

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(1) Determine whether the given matrices are diagonalizable or not. If so, then find its diagonalization (it means to find the diagonal matrix D that it is similar to, as well as the change of basis matrix P).
(a) A = eginpmatrix 2 -1 -1 2 endpmatrix
(b) A = eginpmatrix -3 2 -2 1 endpmatrix
(c) A = eginpmatrix 3 -2 -4 8 -7 -16 -3 3 7 endpmatrix
(d) A = eginpmatrix 3 -1 -1 -12 0 5 4 -2 -1 endpmatrix

Added by Jeffrey I.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Solved by Expert Linda Hand

Step 1

The characteristic equation is: $(2 - \lambda)(2 - \lambda) - (3)(0) = (\lambda - 2)^2 = 0$ There is only one eigenvalue: $\lambda_1 = 2$ Now, let's find the eigenvectors for $\lambda_1 = 2$: $(A - 2I)v = 0$ $\begin{bmatrix} 0 & 3 \\ 0 & 0 \end{bmatrix} Show more…

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(1) Determine whether the given matrices are diagonalizable or not. If so, then find its diagonalization (it means to find the diagonal matrix D that it is similar to, as well as the change of basis matrix P).

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