Test 1 study guide

# Test 1 study guide - Elementary Row Operations 1...

• Notes
• 4
• 100% (10) 10 out of 10 people found this document helpful

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

Elementary Row Operations: 1. Interchange two rows 2. Multiply a row by a nonzero real number 3. Replace a row by its sum with a multiple of another row Over-determined System : More equations than unknowns. In R 2 each equation represents a line, usually inconsistent. Underdetermined System: A system with fewer equations than unknowns. Usually consistent with infinitely many solutions. Inconsistent System: A system with no solutions. Consistent System: A system with one or infinitely many solutions. Reduced Row Echelon Form: 1. If the first nonzero entry in each nonzero row is 1. 2. If row k does not consists entirely of zeros, the number of leading zero entries in row k+1 is greater than the number of leading zero entries in row k. 3. If there are rows whose entries are all zero, they are below the rows having nonzero entries. Matrix-vector multiplication : If A is an mxn matrix and x is a vector in R n then Ax = x 1 a 1 + x 2 a 2 + … + x n a n Consistency Theorem: A linear system Ax=b is consistent if and only if b can be written as a linear combination of the column vectors of A.

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

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