2. (a) Evaluate the following 4x4 determinant using the method of cofactors taught in class, showing your work. In the process, use the shortcut methods that were also taught for 3x3 and 2x2 cases where appropriate: 4 3 2 2 7 -3 12 2 -1 N112 01 0 1 21 (b) For what linear systems does the determinant in part (a) tell us something about the solution(s)? What exactly does it tell us? (c) Find the same determinant using an alternate method:
2. (a) Evaluate the following 4x4 determinant using the method of cofactors taught in class, showing your work. In the process, use the shortcut methods that were also taught for 3x3 and 2x2 cases where appropriate: 4 3 2 2 7 -3 12 2 -1 N112 01 0 1 21 (b) For what linear systems does the determinant in part (a) tell us something about the solution(s)? What exactly does it tell us? (c) Find the same determinant using an alternate method:
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:ences Mailings Review View Help
5
EEEEE
三三三三
T<
V
Search
Paragraph
v
¶
Normal
|1
Accessibilite Good to go
2. (a) Evaluate the following 4x4 determinant using the method of cofactors taught in
class, showing your work. In the process, use the shortcut methods that were also
taught for 3x3 and 2x2 cases where appropriate:
-1
No Spacing
4
0
3
2
1 0
2 7 -3 1
12 2 2 21
Styles
Headi
(b) For what linear systems does the determinant in part (a) tell us something about the
solution(s)? What exactly does it tell us?
(c) Find the same determinant using an alternate method:
Step 1: convert the matrix to a triangular matrix using row operations, keeping
track of how each operation will change the determinant, if applicable
Step 2: find the determinant of the result using the rule for triangular matrices
Step 3: find the determinant of the original matrix by noting how the determinant
was changed by each operation in step 1
Reminder of the rules for how row operations change the determinant:
if two rows of a matrix are equal, the determinant is zero
if two rows of a matrix are interchanged, the determinant changes sign
if a row is multiplied by a constant, the determinant is multiplied by the same
if a multiple of a row is added to another row, the determinant is unchanged
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
