[amp_mcq option1=”positive” option2=”zero” option3=”negative” option4=”imaginary” correct=”option1″]<\/p>\n
The correct answer is $\\boxed{\\text{B. zero}}$.<\/p>\n
A singular matrix is a square matrix that has at least one zero eigenvalue. This means that there exists at least one nonzero vector $v$ such that $Av=0$. In other words, the matrix $A$ does not have an inverse.<\/p>\n
The eigenvalues of a matrix are the roots of its characteristic polynomial. The characteristic polynomial of a singular matrix is a polynomial of degree at least one with at least one root equal to zero. Therefore, at least one eigenvalue of a singular matrix must be zero.<\/p>\n
The other options are incorrect because they are not always true for singular matrices. A singular matrix can have positive, negative, or imaginary eigenvalues, but it must have at least one zero eigenvalue.<\/p>\n","protected":false},"excerpt":{"rendered":"
[amp_mcq option1=”positive” option2=”zero” option3=”negative” option4=”imaginary” 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-20036","post","type-post","status-publish","format-standard","hentry","category-linear-algebra","no-featured-image-padding"],"yoast_head":"\n