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d. \( (8 \mathrm{pts}) \) Verify that \( X=\left[\begin{array}{cccc}1 & -1 & -7 & 0 \\ 0 & 1 & 2 & -1 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & -2\end{array}\right] \) is the matrix of eigenvectors and determine which eigenvalue corresponds to each column vector from \( X \). (Hint: use \( A \mathbf{x}_{i}=\lambda_{i} \mathbf{x}_{i}, i=1,2,3 \) and 4 such that the eigenvalues match the answers from (b)) e. ( 6 pts ) Determine whether \( X \) is singular or invertible. If invertible, find \( X^{-1} \) using either Gauss-Jordan elimination or the matrix of cofactors. f. (1 pts) Based on your results of part (d) and without calculation write the product of \( X^{-1} A X \).

          d. \( (8 \mathrm{pts}) \) Verify that \( X=\left[\begin{array}{cccc}1 & -1 & -7 & 0 \\ 0 & 1 & 2 & -1 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & -2\end{array}\right] \) is the matrix of eigenvectors and determine which eigenvalue corresponds to each column vector from \( X \). (Hint: use \( A \mathbf{x}_{i}=\lambda_{i} \mathbf{x}_{i}, i=1,2,3 \) and 4 such that the eigenvalues match the answers from (b))
e. ( 6 pts ) Determine whether \( X \) is singular or invertible. If invertible, find \( X^{-1} \) using either Gauss-Jordan elimination or the matrix of cofactors.
f. (1 pts) Based on your results of part (d) and without calculation write the product of \( X^{-1} A X \).

d. (8 pts) Verify that X=[
1 -1 -7 0
0 1 2 -1
0 0 1 0
0 0 0 -2
] is the matrix of eigenvectors and determine which eigenvalue corresponds to each column vector from X. (Hint: use A 𝐱i=λi𝐱i, i=1,2,3 and 4 such that the eigenvalues match the answers from (b))
e. ( 6 pts ) Determine whether X is singular or invertible. If invertible, find X^-1 using either Gauss-Jordan elimination or the matrix of cofactors.
f. (1 pts) Based on your results of part (d) and without calculation write the product of X^-1 A X.

Added by Margaret P.

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