Exam (elaborations)
MAT2611 ASSIGNMENT 9 2023
- Course
- MAT2611 - Linear Algebra
- Institution
- University Of South Africa
MAT2611 ASSIGNMENT 9 2023. 100% CORRECT questions, answers, workings and explanations. for assistance.
[Show more]
Content preview
MAT2611 ASSIGNMENT 9 2023, ASSIGNMENT 09
Due date: Friday, 11 August 2023
Problem 31. Suppose S = fv1; v2g is a basis of R2; where v1 = (1; 1) and
v2 = (2; 0).Let T : R 2 ! R 2 be the linear operator for which
T (v1) = (3; 2) and T (v
2) = ( 1; 0) :
Find a formula for T (x; y) ; and compute T (3;
2).
[25 marks]
Problem 32. Let T be multiplication by the matrix
2 3
2 0 1
A=4 4 0 25
20 0 0
1. Find a basis for the range of T .
2. Find a basis for the kernel of T .
3. Find the rank and nullity of T .
4. Find the rank and nullity of A.
[25 marks]
Problem 33. Let A be a 4 6 matrix with rank 3.
(1) What is the dimension of the solution space of Ax = 0.
(2) Is Ax = b consistent for all vectors b in4?RExplain.
[25 marks]
Problem 34. Let v1; v2; and v3 be vectors in a vector space V; and let
T : V ! R 3 be a linear transformation for which
T (v1) = (1; 3; 2) ; T (v2) = (0; 1; 3) ; T (v3) = ( 1; 2; 1) :
Find T (2v1 v2 + 3v3).
[25 marks]
[Total:100 marks]
–End of assignment –
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 EFT, 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 this summary from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller LOVELY01. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy this summary for R48,62. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
67474 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy summaries for 14 years now