[amp_mcq option1=”4″ option2=”3″ option3=”2″ option4=”1″ correct=”option1″]<\/p>\n
The correct answer is $\\boxed{\\text{D}}$.<\/p>\n
An eigenvalue of a square matrix $M$ is a number $\\lambda$ such that there exists a nonzero vector $v$ such that $Mv=\\lambda v$. In other words, an eigenvalue is a number that $M$ maps to itself when multiplied by a nonzero vector.<\/p>\n
If the entries in each column of a square matrix $M$ add up to 1, then $M$ is a stochastic matrix. A stochastic matrix is a matrix with non-negative entries such that the sum of the entries in each row is 1.<\/p>\n
It can be shown that any stochastic matrix has at least one eigenvalue equal to 1. This is because the vector $v$ with all entries equal to 1 is a solution to the equation $Mv=\\lambda v$ for any $\\lambda$.<\/p>\n
Therefore, if the entries in each column of a square matrix $M$ add up to 1, then an eigenvalue of $M$ is $\\boxed{\\text{1}}$.<\/p>\n
Here is a more detailed explanation of each option:<\/p>\n
[amp_mcq option1=”4″ option2=”3″ option3=”2″ option4=”1″ correct=”option1″]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[489],"tags":[],"class_list":["post-19999","post","type-post","status-publish","format-standard","hentry","category-linear-algebra","no-featured-image-padding"],"yoast_head":"\n