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Matrix A is factored in the form PDP?¹. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace.\ $egin{bmatrix} 3 & 0 & -18 \ 9 & 6 & 54 \ 0 & 0 & 6 end{bmatrix} = egin{bmatrix} -6 & 0 & -1 \ 0 & 1 & 3 \ 1 & 0 & 0 end{bmatrix} egin{bmatrix} 6 & 0 & 0 \ 0 & 6 & 0 \ 0 & 0 & 3 end{bmatrix} egin{bmatrix} 0 & 0 & 1 \ 3 & 1 & 18 \ -1 & 0 & -6 end{bmatrix}$\Select the correct choice below and fill in the answer boxes to complete your choice. (Use a comma to separate vectors as needed.)\A. There is one distinct eigenvalue, $lambda = 3$. A basis for the corresponding eigenspace is $egin{bmatrix} -1 \ 3 \ 0 end{bmatrix}$.\B. In ascending order, the two distinct eigenvalues are $lambda_1 = Box$ and $lambda_2 = Box$. Bases for the corresponding eigenspaces are ${Box}$ and ${Box}$, respectively. C. In ascending order, the three distinct eigenvalues are $lambda_1 = Box$, $lambda_2 = Box$, and $lambda_3 = Box$. Bases for the corresponding eigenspaces are ${Box}$, ${Box}$, and ${Box}$, respectively.

          Matrix A is factored in the form PDP?¹. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace.\
$egin{bmatrix} 3 & 0 & -18 \ 9 & 6 & 54 \ 0 & 0 & 6 end{bmatrix} = egin{bmatrix} -6 & 0 & -1 \ 0 & 1 & 3 \ 1 & 0 & 0 end{bmatrix} egin{bmatrix} 6 & 0 & 0 \ 0 & 6 & 0 \ 0 & 0 & 3 end{bmatrix} egin{bmatrix} 0 & 0 & 1 \ 3 & 1 & 18 \ -1 & 0 & -6 end{bmatrix}$\Select the correct choice below and fill in the answer boxes to complete your choice.
(Use a comma to separate vectors as needed.)\A. There is one distinct eigenvalue, $lambda = 3$. A basis for the corresponding eigenspace is $egin{bmatrix} -1 \ 3 \ 0 end{bmatrix}$.\B. In ascending order, the two distinct eigenvalues are $lambda_1 = Box$ and $lambda_2 = Box$. Bases for the corresponding eigenspaces are ${Box}$ and ${Box}$, respectively.
C. In ascending order, the three distinct eigenvalues are $lambda_1 = Box$, $lambda_2 = Box$, and $lambda_3 = Box$. Bases for the corresponding eigenspaces are ${Box}$, ${Box}$, and ${Box}$, respectively.

Matrix A is factored in the form PDP?¹. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace.eginbmatrix 3 0 -18 9 6 54 0 0 6 endbmatrix = eginbmatrix -6 0 -1 0 1 3 1 0 0 endbmatrix eginbmatrix 6 0 0 0 6 0 0 0 3 endbmatrix eginbmatrix 0 0 1 3 1 18 -1 0 -6 endbmatrixthe correct choice below and fill in the answer boxes to complete your choice.
(Use a comma to separate vectors as needed.). There is one distinct eigenvalue, lambda = 3. A basis for the corresponding eigenspace is eginbmatrix -1 3 0 endbmatrix.. In ascending order, the two distinct eigenvalues are lambda1 = Box and lambda2 = Box. Bases for the corresponding eigenspaces are Box and Box, respectively.
C. In ascending order, the three distinct eigenvalues are lambda1 = Box, lambda2 = Box, and lambda3 = Box. Bases for the corresponding eigenspaces are Box, Box, and Box, respectively.

Added by Caitlin R.

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