
Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
This is the Past Exam of Linear Algebra which includes Vectors, Angle, System, Factorization, Matrix Pascal, Matrix, Reflects Vectors, Line Making Angle, Same Line etc. Key important points are: Subspaces Associated, Complete Solution, System, Factorization, Determinant, Solve, Basis, Associated, Factored, Column Space
Typology: Exams
1 / 1
This page cannot be seen from the preview
Don't miss anything!
This take-home exam is due on Friday, November 14 by 5 PM. You may consult the textbook (or any other book) and any class notes and handouts, but please do not discuss any details of this exam with anyone except me! Please sign the bottom of this sheet and turn it in with your exam. You may ask me questions about the exam, but I reserve the right to give unsatisfying answers. Matrix multiplications and reduced row echelon forms may be done on MATLAB or a calculator, but please show all other work.
x 1 x 2 x 3 x 4 x 5
What is the factored form of A that displays these bases?
 and
 span a 3-dimensional subspace of R^4. Find an orthonormal
basis for it.
,^ ~v 2 =
, and^ ~v 3 =
, and let^ S^ be the subspace of^ R^4 spanned by
~v 1 and ~v 2. Find the matrix P that projects vectors in R^4 onto S, and the matrix R that reflects through S. Find also the projection ~p of ~v 3 onto S and the reflection ~r of ~v 3 through S.
is a projection matrix.
Find a basis for the subspace T of R^6 that P projects onto, and a basis for T ā„^ (the orthogonal complement of T ).
I affirm that I did not receive help from another person in doing this exam, nor did I give help to another student in the class.
(signed)