{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Stitz-Zeager_College_Algebra_e-book

Equating coecients we get the system a 2b 1 a b 5 this

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: sing row operations. What does all of this mean for a system of linear equations? Theorem 8.6 tells us that if we write the system in the form AX = B , then if the coefficient matrix A is invertible, there is only one solution to the system − that is, if A is invertible, the system is consistent and independent.5 We 4 If this proof sounds familiar, it should. See the discussion following Theorem 5.2 on page 295. It can be shown that a matrix is invertible if and only if when it serves as a coefficient matrix for a system of equations, the system is always consistent independent. It amounts to the second property in Theorem 8.6 where the matrices B are restricted to being n × 1 matrices. We note for the interested reader that, owing to how matrix multiplication is defined, being able to find unique solutions to AX = B for n × 1 matrices B gives you the same statement about solving such equations for n × r matrices − since we can find a unique solution to them one column at a time. 5 498 System...
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