Difference between revisions of "031 Review Part 1, Problem 4"
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Kayla Murray (talk | contribs) (Created page with "<span class="exam">True or false: If all the entries of a <math style="vertical-align: 0px">7\times 7</math> matrix <math style="vertical-align: 0px">A</math...") |
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| − | <span class="exam">True or false: If | + | <span class="exam"> True or false: If <math style="vertical-align: 0px">A</math> is invertible, then <math style="vertical-align: 0px">A</math> is diagonalizable. |
{| class="mw-collapsible mw-collapsed" style = "text-align:left;" | {| class="mw-collapsible mw-collapsed" style = "text-align:left;" | ||
Revision as of 12:15, 9 October 2017
True or false: If is invertible, then is diagonalizable.
| Solution: |
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| First, we switch to the limit to so that we can use L'Hopital's rule. |
| So, we have |
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Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{array}{rcl} \displaystyle{\lim_{x \rightarrow \infty}\frac{3-2x^2}{5x^2 + x +1}} & \overset{L'H}{=} & \displaystyle{\lim_{x \rightarrow \infty}\frac{-4x}{10x+1}}\\ &&\\ & \overset{L'H}{=} & \displaystyle{\frac{-4}{10}}\\ &&\\ & = & \displaystyle{-\frac{2}{5}}. \end{array}} |
| Final Answer: |
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| False |