(1 point) The matrix \begin{bmatrix} 9 & -2 & -10 \\ 0 & -3 & 0 \\ 5 & -2 & -6 \end{bmatrix} has eigenvalues -3, -1, and 4. Find its basic eigenvectors.
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For the eigenvalue -3, we need to solve the equation (A + 3I)x = 0, where I is the identity matrix. This gives us: (-2+3)x1 - 10x2 - 3x3 = 0 -3x1 + (-2+3)x2 + 6x3 = 0 x1, x2, x3 are the components of the eigenvector x. Simplifying these equations, we get: x1 - Show more…
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