Without calculation, find one eigenvalue and two linearly independent eigenvectors of A = egin{bmatrix} 2 & 2 & 2 \ 2 & 2 & 2 \ 2 & 2 & 2 end{bmatrix}. Justify your answer. One eigenvalue of A is ? = because
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This means that the rows (and columns) of the matrix are linearly dependent. In a matrix with linearly dependent rows or columns, the determinant of the matrix is zero. The determinant of a matrix is also the product of its eigenvalues. Therefore, if the Show more…
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Without calculation, find one eigenvalue and two linearly independent eigenvectors of A. Justify your answer. One eigenvalue of A is λ= because Two linearly independent eigenvectors of A are because (Use a comma to separate answers as needed.) each vector is in the column space of A. the entries of each vector are equal. the entries of each vector are positive. the entries of each vector sum to 0.
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Let $A=\left[\begin{array}{rrr}{2} & {-1} & {1} \\ {-1} & {2} & {-1} \\ {1} & {-1} & {2}\end{array}\right], \quad \mathbf{v}_{1}=\left[\begin{array}{r}{-1} \\ {0} \\ {1}\end{array}\right], \quad$ and $\quad \mathbf{v}_{2}=$ $\left[\begin{array}{r}{1} \\ {-1} \\ {1}\end{array}\right] .$ Verify that $\mathbf{v}_{1}$ and $\mathbf{v}_{2}$ are eigenvectors of $A .$ Then orthogonally diagonalize $A$
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