notes1-7

notes1-7 - SECTION 1.7 LINEAR INDEPENDENCE We know that 3...

This preview shows pages 1–3. Sign up to view the full content.

SECTION 1.7 LINEAR INDEPENDENCE We know that 3 vectors in R 4 cannot span R 4 . What about 4 vectors, say v 1 , v 2 , v 3 , v 4 ? If, say, v 4 is a LC of the others, then what can we say about Span { v 1 , v 2 , v 3 , v 4 } ? LINEARLY DEPENDENT LISTS OF VECTORS. A list of vectors is linearly de- pendent if we can throw one of the vectors away, and the span of the resulting smaller list is the same as the span of the original list. In addition we say that a list consisting only of the zero vector is linearly dependent. WHAT ABOUT A LIST OF TWO VECTORS? WHAT ABOUT A LIST OF, SAY, p VECTORS? A list of two or more vectors is linearly dependent exactly when one of the vectors in the list is a linear combination of the others in the list.

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

View Full Document
Rewrite the linear dependence property in terms of linear combinations of all the vectors in the list. The linear dependence of a list of two or more vectors can be expressed in three equivalent ways.
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