A square matrix A is invertible if and only if det A + 0. Use the theorem above to find all values of k for which A is invertible. (Enter your answers as a comma-separated list.) k-k 0 k+ 1 5 1 k -15 k-1 A =
A square matrix A is invertible if and only if det A + 0. Use the theorem above to find all values of k for which A is invertible. (Enter your answers as a comma-separated list.) k-k 0 k+ 1 5 1 k -15 k-1 A =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Matrix Invertibility Theorem**
To determine the invertibility of a square matrix \( A \), the determinant \(\det A\) must be non-zero.
**Given Matrix A:**
\[
A = \begin{bmatrix}
k & -k & 5 \\
0 & k + 1 & 1 \\
k & -15 & k - 1
\end{bmatrix}
\]
**Exercise:**
Use the theorem to find all values of \( k \) that make the matrix \( A \) invertible. Enter your answers as a comma-separated list.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F992f5037-f1cc-4483-8aa3-731b184958ad%2F1e3d534f-83a8-419c-9a4d-b5dca91b4090%2Fqa07bro_processed.png&w=3840&q=75)
Transcribed Image Text:**Matrix Invertibility Theorem**
To determine the invertibility of a square matrix \( A \), the determinant \(\det A\) must be non-zero.
**Given Matrix A:**
\[
A = \begin{bmatrix}
k & -k & 5 \\
0 & k + 1 & 1 \\
k & -15 & k - 1
\end{bmatrix}
\]
**Exercise:**
Use the theorem to find all values of \( k \) that make the matrix \( A \) invertible. Enter your answers as a comma-separated list.
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