




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
INSTRUCTIONS. • This test has 6 problems on 6 pages, worth a total of. 100 points. Check if you have all 6 pages with ques-.
Typology: Exercises
1 / 8
This page cannot be seen from the preview
Don't miss anything!





Whose discussion section are you enrolled in? Circle one. Yash Lodha Wai-kit Yeung At what time is the discussion section you enrolled in? Circle one. 1:25-2:15pm 2:30-3:20pm 3:35-4:25pm
Total: / 100
Academic integrity is expected of all Cornell University students at all times, whether in the presence or absence of members of the faculty. Understanding this, I declare I shall not give, use, or receive unauthorized aid in this exam- ination. Please sign below to indicate that you have read and agree to these instructions.
Signature of Student
A =
Compute a basis for each of the following spaces:
(a) The column space of A. (b) The row space of A. (c) The null space of A.
A =
(a) Calculate the determinant of A. (b) Let ~r 1 , ~r 2 and ~r 3 be the 3 rows of A. What is the volume of the parallelepiped spanned by ~r 1 , 2~r 2 and 3~r 3? (c) Consider the linear transformation T (~x) = A~x. What is the volume of the paral- lelepiped spanned by T (~r 1 ), T (~r 2 ) and T (~r 3 )?
(a) Show that L is a vector subspace. (b) Compute a basis for L.
(c) Find the coordinates of T
x y z
(^) = x + y + z in the basis from part (b).
(a) If A and B are similar matrices then they have the same eigenvalues.
(b) If A, P and Q are 2 × 2 matrices such that
= P −^1 AP = Q−^1 AQ, then P and Q are scalar multiples of each other. (c) There is no 3 × 3 matrix A such that both A and A − I 3 have null spaces of dimension 2. (d) Given a matrix A and a vector ~x, if A~x is an eigenvector of A then ~x is an eigenvector for A.
This page is for scratch work, it will not be graded unless you point us here from the page where the question was posed.