Difference between revisions of "031 Review Part 1, Problem 1"

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(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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!Solution: &nbsp;  
 
!Solution: &nbsp;  
 
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|First, we switch to the limit to <math style="vertical-align: 0px">x</math> so that we can use L'Hopital's rule.
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|If all the entries of &nbsp;<math style="vertical-align: 0px">A</math>&nbsp; are &nbsp;<math style="vertical-align: -4px">7,</math>&nbsp; then all the rows of &nbsp;<math style="vertical-align: 0px">A</math>&nbsp; are identical.
 
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|So, we have
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|So, when you row reduce &nbsp;<math style="vertical-align: -4px">A,</math>&nbsp; it is row equivalent to a matrix &nbsp;<math style="vertical-align: -4px">B,</math>&nbsp; where &nbsp;<math style="vertical-align: 0px">B</math>&nbsp; contains a row of zeros.
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|Then,
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::<math>\text{det } B=0.</math>
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|But, &nbsp;<math style="vertical-align: -1px">\text{det }A</math>&nbsp; is a scalar multiple of &nbsp;<math style="vertical-align: -1px">\text{det }B.</math>&nbsp;
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|So,
 
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&nbsp; &nbsp; &nbsp; &nbsp;<math>\begin{array}{rcl}
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::<math>\text{det }A=0</math>
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\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}}\\
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&&\\
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|and the statement is false.
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& \overset{L'H}{=} & \displaystyle{\frac{-4}{10}}\\
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&&\\
 
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& = & \displaystyle{-\frac{2}{5}}.
 
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\end{array}</math>
 
 
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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
!Final Answer: &nbsp;  
 
!Final Answer: &nbsp;  
 
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|&nbsp;&nbsp; &nbsp; &nbsp; False
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|&nbsp;&nbsp; &nbsp; &nbsp; FALSE
 
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[[031_Review_Part_1|'''<u>Return to Sample Exam</u>''']]
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[[031_Review_Part_1|'''<u>Return to Review Problems</u>''']]

Latest revision as of 12:00, 15 October 2017

True or false: If all the entries of a    matrix    are    then    must be  

Solution:  
If all the entries of    are    then all the rows of    are identical.
So, when you row reduce    it is row equivalent to a matrix    where    contains a row of zeros.
Then,
But,    is a scalar multiple of   
So,
and the statement is false.


Final Answer:  
       FALSE

Return to Review Problems

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