Skip to main content
Mathematics

Return to Question

added 10 characters in body; edited title
Source Link
Calvin Khor
Calvin Khor
  • 36.6k
  • 6
  • 48
  • 105

Is this 3 x 3$3 \times 3$ matrix with 2$2$ eigenvalues diagonalizable

$$ \begin{matrix} 1 & 1 & 0 \\ 3 & 0 & 1 \\ 1 & -1 & 2 \\ \end{matrix} $$$$ \begin{bmatrix} 1 & 1 & 0 \\ 3 & 0 & 1 \\ 1 & -1 & 2 \\ \end{bmatrix} $$

Is the 3$3$ by 3$3$ matrix above diagonalizable given the eigenvalues -1$-1$ and 2$2$? There are only 2 eigenvalue$2$ eigenvalues so the one with the multiplicity of two needs a full rank eigenspace for this to be diagonalizable. I think there should be a way to tell from the matrix alone whether that's possible without doing all the row operations, but I'm not sure what I should be looking for.

Is this 3 x 3 matrix with 2 eigenvalues diagonalizable

$$ \begin{matrix} 1 & 1 & 0 \\ 3 & 0 & 1 \\ 1 & -1 & 2 \\ \end{matrix} $$

Is the 3 by 3 matrix above diagonalizable given the eigenvalues -1 and 2? There are only 2 eigenvalue so the one with the multiplicity of two needs a full rank eigenspace for this to be diagonalizable. I think there should be a way to tell from the matrix alone whether that's possible without doing all the row operations, but I'm not sure what I should be looking for.

Is this $3 \times 3$ matrix with $2$ eigenvalues diagonalizable

$$ \begin{bmatrix} 1 & 1 & 0 \\ 3 & 0 & 1 \\ 1 & -1 & 2 \\ \end{bmatrix} $$

Is the $3$ by $3$ matrix above diagonalizable given the eigenvalues $-1$ and $2$? There are only $2$ eigenvalues so the one with the multiplicity two needs a full rank eigenspace for this to be diagonalizable. I think there should be a way to tell from the matrix alone whether that's possible without doing all the row operations, but I'm not sure what I should be looking for.

edited tags
Link
RobPratt
RobPratt
  • 52.5k
  • 4
  • 33
  • 71
Source Link
willyx888
willyx888
  • 481
  • 2
  • 12

Is this 3 x 3 matrix with 2 eigenvalues diagonalizable

$$ \begin{matrix} 1 & 1 & 0 \\ 3 & 0 & 1 \\ 1 & -1 & 2 \\ \end{matrix} $$

Is the 3 by 3 matrix above diagonalizable given the eigenvalues -1 and 2? There are only 2 eigenvalue so the one with the multiplicity of two needs a full rank eigenspace for this to be diagonalizable. I think there should be a way to tell from the matrix alone whether that's possible without doing all the row operations, but I'm not sure what I should be looking for.