Difference between revisions of "031 Review Part 3, Problem 10"

From Grad Wiki
Jump to navigation Jump to search
Line 4: Line 4:
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
!Foundations:    
 
!Foundations:    
 +
|-
 +
|An eigenvector &nbsp;<math style="vertical-align: 0px">\vec{x}</math>&nbsp; of a matrix &nbsp;<math style="vertical-align: 0px">A</math>&nbsp; is a nonzero vector such that
 
|-
 
|-
 
|
 
|
 +
::<math>A\vec{x}=\lambda\vec{x}</math>
 +
|-
 +
|for some scalar &nbsp;<math style="vertical-align: 0px">\lambda.</math>
 
|}
 
|}
  

Revision as of 20:57, 10 October 2017

Show that if    is an eigenvector of the matrix product  Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle AB}   and  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 B\vec{x}\ne \vec{0},}   then  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 B\vec{x}}   is an eigenvector of  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 BA.}


Foundations:  
An eigenvector  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 \vec{x}}   of a matrix  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 A}   is a nonzero vector such that
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 A\vec{x}=\lambda\vec{x}}
for some scalar  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 \lambda.}


Solution:

Step 1:  
Step 2:  


Final Answer:  
      

Return to Sample Exam

Retrieved from "https://gradwiki.math.ucr.edu/index.php?title=031_Review_Part_3,_Problem_10&oldid=3599"