MATH 551 Final: MATH 551 KSU FinalExam 05 07
15 Feb 2019
School
Department
Course
Professor
Name Lecture Time (check one): MW 10:30
MW 1:30
APPLIED MATRIX THEORY
Final Exam
May 7, 2018
Below you will find 6 problems, with scores indicated in parentheses. No books or notes, and
no electronic devices are allowed. Solve the problems in the space provided. When writing a
solution to a problem, show all work, and justify your steps.
Problem 1. (10 points) Find the eigenvalues of the matrix
A=
1 0 −2
3−4 5
0 0 6
.
1
Problem 2. (10 points) Find a basis for the column space col(A) of the matrix
A=
1 2 2 3 4
2 4 3 −1 0
3 6 7 −3 2
.
Based on your finding, determine the rank of A.
2
Problem 3. (10 points) Find a basis for the null space ker(A) of the matrix
A=
1234
−4−3−2−1
7777
.
Based on your finding, determine the rank of A.
3
Document Summary
Below you will nd 6 problems, with scores indicated in parentheses. No books or notes, and no electronic devices are allowed. When writing a solution to a problem, show all work, and justify your steps. Problem 1. (10 points) find the eigenvalues of the matrix. Problem 2. (10 points) find a basis for the column space col(a) of the matrix. Problem 3. (10 points) find a basis for the null space ker(a) of the matrix. Based on your nding, determine the rank of a. Problem 4. (10 points) the eigenvalues of the matrix. 3 are 1 = 1 and 2 = 2. Find the corresponding eigenspaces e 1(a) and e 2(a) and their dimensions. Based on your ndings, decide if a is (or is not) diagonalizable. Problem 5. (10 points) consider the following subspace in r4: Problem 6. (10 points) consider the following subspace in r4: Compute projw( v ) (that is, the projection of v onto w).
