



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
The solutions to exam 2 for a linear algebra course, mat340. It includes problems on expressing vectors in different bases, finding matrix representations of linear transformations, and calculating the row space, column space, and null space of matrices. Students are expected to have a solid understanding of linear algebra concepts.
Typology: Exams
1 / 6
This page cannot be seen from the preview
Don't miss anything!
MAT340 Exam 2 Due 14 November, 2006 Prof. Thistleton
You may consult written sources such as textbooks or your class notes as you work through this exam. You may not, however, work with or receive help from anyone on this exam.
V = {v 1 , v 2 , v 3 } where v 1 =
, v 2 =
, v 3 =
and
U = {u 1 , u 2 , u 3 } where u 1 =
, u 2 =
, u 3 =
.
(a) Express x =
in terms of basis V.
(b) Express x =
in terms of basis^ U^.
(c) Find the matrix S which transforms vectors in terms of basis V to basis U and demon- strate that this works for your vector x.
L(x) = L([x 1 , x 2 , x 3 ]T^ ) = [2x 1 − x 3 , x 2 + x 3 , x 1 − x 2 ]T
Find the matrix representation of this linear transformation with respect to the standard basis and use it to calculate L([1, 1 , 1]T^ ).
L([3, −2]T^ ) = [2, 2]T^ and L([2, 1]T^ ) = [3, 5]T
then calculate L([10, −9]T^ ).
(d) Show that B = S−^1 AS.
Find a basis for the row space, the column space and the null space of A.