-9 Using only a simple calculator, find the values of k such that det(M) = 0, where M = 1 your answer, enter the SUM of the value(s) of k that satisfy this condition. 1 k 01 1. As 1 2
-9 Using only a simple calculator, find the values of k such that det(M) = 0, where M = 1 your answer, enter the SUM of the value(s) of k that satisfy this condition. 1 k 01 1. As 1 2
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
![**Problem Statement:**
Using only a simple calculator, find the values of \( k \) such that \( \text{det}(M) = 0 \), where
\[
M = \begin{bmatrix}
-9 & k & 0 \\
1 & 1 & k \\
1 & 1 & 2
\end{bmatrix}
\]
As your answer, enter the **SUM** of the value(s) of \( k \) that satisfy this condition.
---
**Instructions:**
To solve this problem, you need to calculate the determinant of the matrix \( M \) and find the values of \( k \) that make the determinant zero.
**Steps to Solve:**
1. Compute the determinant of the matrix \( M \).
2. Set the determinant equal to zero and solve for \( k \).
3. Find all possible values of \( k \).
4. Add the values of \( k \) to get the sum.
**Note:** Show your work clearly to ensure understanding, and use just a simple calculator for arithmetic operations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18574973-f25e-4ab8-b7d6-6007b5b87fc4%2F24ae7604-e804-4411-b44e-79042f7bc6c8%2F19clb3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Using only a simple calculator, find the values of \( k \) such that \( \text{det}(M) = 0 \), where
\[
M = \begin{bmatrix}
-9 & k & 0 \\
1 & 1 & k \\
1 & 1 & 2
\end{bmatrix}
\]
As your answer, enter the **SUM** of the value(s) of \( k \) that satisfy this condition.
---
**Instructions:**
To solve this problem, you need to calculate the determinant of the matrix \( M \) and find the values of \( k \) that make the determinant zero.
**Steps to Solve:**
1. Compute the determinant of the matrix \( M \).
2. Set the determinant equal to zero and solve for \( k \).
3. Find all possible values of \( k \).
4. Add the values of \( k \) to get the sum.
**Note:** Show your work clearly to ensure understanding, and use just a simple calculator for arithmetic operations.
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