Final Exam
12/11/2023
MATH 220
Matrices
Name:
PRINT your name CLEARLY as it appears in CANVAS and LionPath.
PSU Email ID: @psu.edu
Section Instructor:
Section number:
INSTRUCTIONS
Write your initials on the bottom of each page in the indicated space.
Failure to do this may result in a 5 point deduction.
Check that your exam contains 20 questions numbered sequentially on 21
pages.
Answer all your questions in your test booklet, show all of your work, write
legibly, and write your final answer in the box or space provided.
The use of a calculator, cell phone, smartwatch, or any other electronic device
is not permitted during this examination.
The use of scrap paper or notes of any kind is not permitted during this
examination.
Good luck!
Page 1 of 21 Initials:
,You can use this page for overflow scratch work. Please label which problem(s) it pertains to. Only
use this page if you run out of space elsewhere.
Page 2 of 21 Initials:
, 1. (6 points) The matrices below are in echelon form with ∗ representing a nonzero entry. Each aug-
mented matrix represents a linear system. Determine if the system is consistent. If it is consistent,
determine if the solution is unique.
∗ ∗ ∗
(a) 0 ∗ ∗
0 0 0
⃝ Inconsistent
⃝ Consistent with a unique solution
⃝ Consistent with infinitely many solutions
∗ ∗ ∗ ∗ ∗
(b)
0 0 0 ∗ 0
⃝ Inconsistent
⃝ Consistent with a unique solution
⃝ Consistent with infinitely many solutions
∗ ∗ ∗ ∗
(c) 0 ∗ ∗ ∗
0 0 0 ∗
⃝ Inconsistent
⃝ Consistent with a unique solution
⃝ Consistent with infinitely many solutions
Page 3 of 21 Initials:
12/11/2023
MATH 220
Matrices
Name:
PRINT your name CLEARLY as it appears in CANVAS and LionPath.
PSU Email ID: @psu.edu
Section Instructor:
Section number:
INSTRUCTIONS
Write your initials on the bottom of each page in the indicated space.
Failure to do this may result in a 5 point deduction.
Check that your exam contains 20 questions numbered sequentially on 21
pages.
Answer all your questions in your test booklet, show all of your work, write
legibly, and write your final answer in the box or space provided.
The use of a calculator, cell phone, smartwatch, or any other electronic device
is not permitted during this examination.
The use of scrap paper or notes of any kind is not permitted during this
examination.
Good luck!
Page 1 of 21 Initials:
,You can use this page for overflow scratch work. Please label which problem(s) it pertains to. Only
use this page if you run out of space elsewhere.
Page 2 of 21 Initials:
, 1. (6 points) The matrices below are in echelon form with ∗ representing a nonzero entry. Each aug-
mented matrix represents a linear system. Determine if the system is consistent. If it is consistent,
determine if the solution is unique.
∗ ∗ ∗
(a) 0 ∗ ∗
0 0 0
⃝ Inconsistent
⃝ Consistent with a unique solution
⃝ Consistent with infinitely many solutions
∗ ∗ ∗ ∗ ∗
(b)
0 0 0 ∗ 0
⃝ Inconsistent
⃝ Consistent with a unique solution
⃝ Consistent with infinitely many solutions
∗ ∗ ∗ ∗
(c) 0 ∗ ∗ ∗
0 0 0 ∗
⃝ Inconsistent
⃝ Consistent with a unique solution
⃝ Consistent with infinitely many solutions
Page 3 of 21 Initials:
