Evaluate the given determinant after first simplifying the computation by adding an appropriate multiple of some row or column to another. -6 9 1 2-3-5 2 -5 19 Evaluate the determinant. -6 9 1 2-3-5 2 -5 19 (Simplify your answer.) ...
Evaluate the given determinant after first simplifying the computation by adding an appropriate multiple of some row or column to another. -6 9 1 2-3-5 2 -5 19 Evaluate the determinant. -6 9 1 2-3-5 2 -5 19 (Simplify your answer.) ...
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
![### Determinants and Matrix Simplification
**Problem Statement:**
Evaluate the given determinant after first simplifying the computation by adding an appropriate multiple of some row or column to another.
\[ \begin{vmatrix}
-6 & 9 & 1 \\
2 & -3 & -5 \\
2 & -5 & 19 \\
\end{vmatrix} \]
**Steps to Solve:**
1. **Simplify the Matrix:**
- Look for opportunities to add appropriate multiples of one row to another row, which can simplify the calculation of the determinant.
2. **Evaluate the Determinant:**
- Once the matrix is simplified, use the determinant formula for a 3x3 matrix.
\[ \begin{vmatrix}
-6 & 9 & 1 \\
2 & -3 & -5 \\
2 & -5 & 19 \\
\end{vmatrix} = \Box \]
(Fill in the simplified matrix and the computed determinant in the provided box)
**Additional Concepts:**
- **Determinant of a 3x3 Matrix:**
\[ \text{Det} = a(ei - fh) - b(di - fg) + c(dh - eg) \]
Where the matrix is:
\[ \begin{vmatrix}
a & b & c \\
d & e & f \\
g & h & i \\
\end{vmatrix} \]
For our matrix:
\[ a = -6, b = 9, c = 1 \]
\[ d = 2, e = -3, f = -5 \]
\[ g = 2, h = -5, i = 19 \]
- **Row Operations:**
Adding multiples of rows to each other is allowed and does not change the determinant of the matrix, but it can make the matrix easier to work with.
Remember to verify your steps and calculations to ensure the solution is correct. Simplifying the matrix properly can significantly reduce computational complexity.
(Simplify your answer and fill in the provided box.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3a1a8c69-ac20-486b-9f67-8f66504c5494%2Fdeab873f-8e2d-4b0c-ab70-f9c236c890b8%2Fzcjzbfc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Determinants and Matrix Simplification
**Problem Statement:**
Evaluate the given determinant after first simplifying the computation by adding an appropriate multiple of some row or column to another.
\[ \begin{vmatrix}
-6 & 9 & 1 \\
2 & -3 & -5 \\
2 & -5 & 19 \\
\end{vmatrix} \]
**Steps to Solve:**
1. **Simplify the Matrix:**
- Look for opportunities to add appropriate multiples of one row to another row, which can simplify the calculation of the determinant.
2. **Evaluate the Determinant:**
- Once the matrix is simplified, use the determinant formula for a 3x3 matrix.
\[ \begin{vmatrix}
-6 & 9 & 1 \\
2 & -3 & -5 \\
2 & -5 & 19 \\
\end{vmatrix} = \Box \]
(Fill in the simplified matrix and the computed determinant in the provided box)
**Additional Concepts:**
- **Determinant of a 3x3 Matrix:**
\[ \text{Det} = a(ei - fh) - b(di - fg) + c(dh - eg) \]
Where the matrix is:
\[ \begin{vmatrix}
a & b & c \\
d & e & f \\
g & h & i \\
\end{vmatrix} \]
For our matrix:
\[ a = -6, b = 9, c = 1 \]
\[ d = 2, e = -3, f = -5 \]
\[ g = 2, h = -5, i = 19 \]
- **Row Operations:**
Adding multiples of rows to each other is allowed and does not change the determinant of the matrix, but it can make the matrix easier to work with.
Remember to verify your steps and calculations to ensure the solution is correct. Simplifying the matrix properly can significantly reduce computational complexity.
(Simplify your answer and fill in the provided box.)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 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,
