Eigenvalues

**Benny** · Oct4-05, 11:30 AM

I'm experiencing difficulties trying to find the eigenvalues of the follow matrix. The hint is to use an elementary row operation to simplify $LaTeX Code: C - \\lambda I$ but I can't think of a suitable one to use or figure out whether a single row operation will actually make the calculations simpler.

$LaTeX Code: C = \\left[ {\\begin{array}{*{20}c} {0.98} & {0.01} \\\\ {0.02} & {0.99} \\\\ \\end{array}} \\right] $

$LaTeX Code: \\det \\left( {C - \\lambda I} \\right) = 0 \\Rightarrow \\left| {\\begin{array}{*{20}c} {0.98 - \\lambda } & {0.01} \\\\ {0.02} & {0.99 - \\lambda } \\\\ \\end{array}} \\right| = 0 $

Out of desperation, and having seen it being done once(not sure if it is correct) I decided to then subtract the first column from the second column.

$LaTeX Code: \\left| {\\begin{array}{*{20}c} {0.98 - \\lambda } & { - 0.97 + \\lambda } \\\\ {0.02} & {0.97 - \\lambda } \\\\ \\end{array}} \\right| = 0 $

$LaTeX Code: \\left| {\\begin{array}{*{20}c} {1 - \\lambda } & 0 \\\\ {0.02} & {0.97 - \\lambda } \\\\ \\end{array}} \\right| = 0 $

I'm not even sure if subtracting columns from each other was a valid step. I know that subtracting rows is but I'm not sure about columns. I'm just wondering if that step was correct because if it is then I can get the eigenvalues from it fairly easily.

TD · Oct4-05, 11:35 AM

You're doing great! You can even see the eigenvalues right now, l = 1 or l = 0.97