Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![# Determinant Calculation
## Problem Statement
Find the determinant of the matrix below, given that the determinant of another matrix is 8.
\[
\begin{vmatrix}
a & b & c \\
d & e & f \\
g & h & i \\
\end{vmatrix}
= 8
\]
## Matrix for Determinant Calculation
\[
\begin{vmatrix}
a & b & c \\
d & e & f \\
5g & 5h & 5i \\
\end{vmatrix}
\]
## Task
Calculate the determinant of the new matrix:
\[
\begin{vmatrix}
a & b & c \\
d & e & f \\
5g & 5h & 5i \\
\end{vmatrix}
= \boxed{\ } \quad \text{(Simplify your answer.)}
\]
### Explanation
- The matrix provided is a variation of the original matrix with the third row multiplied by 5.
- To solve, use the property of determinants where multiplying a row by a constant multiplies the determinant by that constant.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2724f57d-1ebd-4904-b3e9-94cc6d926852%2F4a60b92f-f297-478e-9ca3-0b8e705cc202%2F3wn33oa_processed.png&w=3840&q=75)
Transcribed Image Text:# Determinant Calculation
## Problem Statement
Find the determinant of the matrix below, given that the determinant of another matrix is 8.
\[
\begin{vmatrix}
a & b & c \\
d & e & f \\
g & h & i \\
\end{vmatrix}
= 8
\]
## Matrix for Determinant Calculation
\[
\begin{vmatrix}
a & b & c \\
d & e & f \\
5g & 5h & 5i \\
\end{vmatrix}
\]
## Task
Calculate the determinant of the new matrix:
\[
\begin{vmatrix}
a & b & c \\
d & e & f \\
5g & 5h & 5i \\
\end{vmatrix}
= \boxed{\ } \quad \text{(Simplify your answer.)}
\]
### Explanation
- The matrix provided is a variation of the original matrix with the third row multiplied by 5.
- To solve, use the property of determinants where multiplying a row by a constant multiplies the determinant by that constant.
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