(g) 1302 3440 2 -2 3 2 1 -3 1 1 4 -1 3 0 (h) 1 -2 3 -12) -5 12 -14 19 -9 22 -20 31 -4 9 -14 15
(g) 1302 3440 2 -2 3 2 1 -3 1 1 4 -1 3 0 (h) 1 -2 3 -12) -5 12 -14 19 -9 22 -20 31 -4 9 -14 15
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
Can you just answer g and h
![**Problem Statement:**
Evaluate the determinant of the following matrices by any legitimate method.
**Matrices:**
(a) \[
\begin{pmatrix}
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & 9 \\
\end{pmatrix}
\]
(b) \[
\begin{pmatrix}
-1 & 3 & 2 \\
4 & -8 & 1 \\
2 & 2 & 5 \\
\end{pmatrix}
\]
(c) \[
\begin{pmatrix}
0 & 1 & 1 \\
1 & 2 & -5 \\
6 & -4 & 3 \\
\end{pmatrix}
\]
(d) \[
\begin{pmatrix}
1 & -2 & 3 \\
-1 & 2 & -5 \\
3 & -1 & 2 \\
\end{pmatrix}
\]
(e) \[
\begin{pmatrix}
i & 2 & -1 \\
3 & 1+i & 2 \\
-2i & 1 & 4-i \\
\end{pmatrix}
\]
(f) \[
\begin{pmatrix}
-1 & 2+i & 3 \\
1-i & i & 1 \\
3i & 2 & -1+i \\
\end{pmatrix}
\]
(g) \[
\begin{pmatrix}
1 & 0 & -2 & 3 \\
-3 & 1 & 1 & 2 \\
0 & 4 & -1 & 1 \\
2 & 3 & 0 & 1 \\
\end{pmatrix}
\]
(h) \[
\begin{pmatrix}
1 & -2 & 3 & -12 \\
-5 & 12 & -14 & 19 \\
-9 & 22 & -20 & 31 \\
-4 & 9 & -14 & 15 \\
\end{pmatrix}
\]
**Instructions for Evaluation:**
Determine the determinants of each given matrix using appropriate methods such as cofactor expansion, row reduction, or other valid approaches for calculating determinants, particularly for larger or complex matrices in this set. Consider properties of determinants such as linearity, row swaps, and factor extraction where beneficial.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F32f77ee0-291c-46d0-b315-80fb2fd096d8%2Fb96e9837-8a56-4920-aa43-d90746903a5a%2Fiwgn2d7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Evaluate the determinant of the following matrices by any legitimate method.
**Matrices:**
(a) \[
\begin{pmatrix}
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & 9 \\
\end{pmatrix}
\]
(b) \[
\begin{pmatrix}
-1 & 3 & 2 \\
4 & -8 & 1 \\
2 & 2 & 5 \\
\end{pmatrix}
\]
(c) \[
\begin{pmatrix}
0 & 1 & 1 \\
1 & 2 & -5 \\
6 & -4 & 3 \\
\end{pmatrix}
\]
(d) \[
\begin{pmatrix}
1 & -2 & 3 \\
-1 & 2 & -5 \\
3 & -1 & 2 \\
\end{pmatrix}
\]
(e) \[
\begin{pmatrix}
i & 2 & -1 \\
3 & 1+i & 2 \\
-2i & 1 & 4-i \\
\end{pmatrix}
\]
(f) \[
\begin{pmatrix}
-1 & 2+i & 3 \\
1-i & i & 1 \\
3i & 2 & -1+i \\
\end{pmatrix}
\]
(g) \[
\begin{pmatrix}
1 & 0 & -2 & 3 \\
-3 & 1 & 1 & 2 \\
0 & 4 & -1 & 1 \\
2 & 3 & 0 & 1 \\
\end{pmatrix}
\]
(h) \[
\begin{pmatrix}
1 & -2 & 3 & -12 \\
-5 & 12 & -14 & 19 \\
-9 & 22 & -20 & 31 \\
-4 & 9 & -14 & 15 \\
\end{pmatrix}
\]
**Instructions for Evaluation:**
Determine the determinants of each given matrix using appropriate methods such as cofactor expansion, row reduction, or other valid approaches for calculating determinants, particularly for larger or complex matrices in this set. Consider properties of determinants such as linearity, row swaps, and factor extraction where beneficial.
Expert Solution
Step 1
We know that determinant of diagonal matrix, upper triangular matrix, lower triangular matrix is the product of elements of its diagonal.
Step by step
Solved in 3 steps with 2 images
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,
