Exam (elaborations)
1.2 Row Reduction and Echelon Forms Questions and answers latest update 2024
- Course
- Institution
1.2 Row Reduction and Echelon Forms Questions and answers latest update 2024
[Show more]
Content preview
1.2 Row Reduction and Echelon FormsA rectangular matrix is in echelon form if it has the following 3 properties: - correct answerAll nonzero
rows are above any rows of all zeros; each leading entry of a row is in a column to the right of the leading
entry of the row above it; all entries in a column below a leading entry are zeros.
leading entry - correct answerleftmost nonzero entry in a nonzero row
If a matrix in echelon form satisfies the following additional conditions, then it is in reduced echelon
form - correct answerthe leading entry in each nonzero row is 1; each leading 1 is the only nonzero entry
in its column.
Each matrix is row equivalent to... - correct answerone and only one reduced echelon matrix
Since the reduced echelon form is unique, the leading entries are... - correct answeralways in the same
positions in any echelon form obtained from a given matrix
Pivot position - correct answera location in a matrix that corresponds to a leading 1 in the reduced
echelon form of a matrix.
Pivot column - correct answercolumn of a matrix that contains a pivot position
pivot - correct answernonzero number in a pivot position that is used as needed to create zeros via row
operations.
A linear system is consistent if and only if the ________ column of the augmented matrix is _____ a ____
_______ -- that is, if and only if an echelon form of the augmented matrix has no row of the form [ 0 ... 0
b] with b nonzero - correct answerrightmost, not, pivot column
If a linear system is consistent, then the solution set contains either (i) a ____ solution, when there are
___ _____ _________, or (ii) infinitely many solutions, when there is at least ___ ____ ________ -
correct answerunique, no free variables, one free variable
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller Schoolflix. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $13.99. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
80202 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now
