C3091418 - 18 Let A and B be n n matrices and let C = AB...

Info icon This preview shows page 1. Sign up to view the full content.

18. Let A and B be n × n matrices and let C = AB . Prove that if B is singular then C must be singular. Proof. Suppose that B is singular. By the part “(b) (a)” of Theorem 1.4.2, ( why this part? ) the equation B x = 0 has a nontrivial solution. That is, there is a vector x 0 6 = 0 such that B x 0 =
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: . Hence, AB x = A ( B x ) = A = . It means that the equation AB x = has a nontrivial solution x 6 = . By the part “(a) ⇒ (b)” of Theorem 1.4.2, ( again, why this part? ) C = AB is singular. / 1...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern