Find the determinant of the t 5 2-9 17 0 0 8 0 0 0 5 5 0 0 0 -1
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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![**Finding the Determinant of a Triangular Matrix**
Determine the determinant of the following triangular matrix:
\[
\begin{bmatrix}
5 & 2 & -9 & 7 \\
0 & 0 & 8 & 0 \\
0 & 0 & 5 & 5 \\
0 & 0 & 0 & -1
\end{bmatrix}
\]
In a triangular matrix (either upper or lower triangular), the determinant is the product of the diagonal elements. Here, the diagonal elements are 5, 0, 5, and -1. Since one of the diagonal elements is zero, the determinant of this matrix is also zero.
\[
\text{Det} = 5 \times 0 \times 5 \times -1 = 0
\]
Thus, the determinant of the given triangular matrix is:
\[
\boxed{0}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F73fb2883-df73-4e37-b7ef-66d24e1d1095%2F540efd3f-3872-40a5-b529-05eda24639dd%2Fyxvdgy4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Finding the Determinant of a Triangular Matrix**
Determine the determinant of the following triangular matrix:
\[
\begin{bmatrix}
5 & 2 & -9 & 7 \\
0 & 0 & 8 & 0 \\
0 & 0 & 5 & 5 \\
0 & 0 & 0 & -1
\end{bmatrix}
\]
In a triangular matrix (either upper or lower triangular), the determinant is the product of the diagonal elements. Here, the diagonal elements are 5, 0, 5, and -1. Since one of the diagonal elements is zero, the determinant of this matrix is also zero.
\[
\text{Det} = 5 \times 0 \times 5 \times -1 = 0
\]
Thus, the determinant of the given triangular matrix is:
\[
\boxed{0}
\]
![**Solve for x:**
(Enter your answers as a comma-separated list.)
\[ \begin{vmatrix}
x - 1 & 3 \\
2 & x - 2
\end{vmatrix} = 0 \]
\( x = \) _________](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F73fb2883-df73-4e37-b7ef-66d24e1d1095%2F540efd3f-3872-40a5-b529-05eda24639dd%2Fyfitct_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Solve for x:**
(Enter your answers as a comma-separated list.)
\[ \begin{vmatrix}
x - 1 & 3 \\
2 & x - 2
\end{vmatrix} = 0 \]
\( x = \) _________
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