031 Review Part 1, Problem 5

True or false: If all the entries of a  $7\times 7$  matrix  $A$  are  $7,$  then  ${\text{det }}A$  must be  $7^{7}.$

Solution:
First, we switch to the limit to $x$ so that we can use L'Hopital's rule.
So, we have
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:
False

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