{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

m235notes19

# m235notes19 - Notes 19 Determinants Lecture November 2011...

This preview shows pages 1–2. Sign up to view the full content.

Notes 19: Determinants Lecture November, 2011 Let A be an n × n matrix. The determinant of A is a number denoted det ( A ) or | A | . It has many uses, but we will use it for one thing. It enables us to decide if a matrix is invertible. Theorem 1 . Let A be an n × n matrix. Then A is invertible if and only if det ( A ) = | A | 6 = 0 . Corollary 1 . Let A be an n × n matrix. The following are equivalent: det ( A ) = 0 . A is not invertible. ker ( A ) 6 = 0 . im ( A ) 6 = R n . Definition 1. Let A be an n × m. the transpose of A is the m × n matrix whose rows are the columns of A. Let A be an n × n matrix. We show how to compute the determinant of A . We do not give a formula for the determinant, but rather a set of rules. We give the value for the determinant for simple matrices and a set of rules that allow us to turn the matrix into one of the simple matrices while keeping track of how the value of the determinant changes. Rule 1: The determinant of a matrix with all zeros above the diagonal is the product of the diagonal entries. The determinant of a matrix with all zeros below the diagonal is

This preview has intentionally blurred sections. Sign up to view the full version.

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

{[ snackBarMessage ]}

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern