Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![**Problem Statement:**
Find the determinant, assuming that:
\[
\begin{vmatrix}
a & b & c \\
d & e & f \\
g & h & i \\
\end{vmatrix} = 2.
\]
**Matrix for Determinant Calculation:**
\[
\begin{vmatrix}
6a & b/7 & -c \\
6d & e/7 & -f \\
6g & h/7 & -i \\
\end{vmatrix}
\]
**Explanation:**
The problem provides two matrices. The determinant of the first \(3 \times 3\) matrix is given as 2. You are required to find the determinant of the second \(3 \times 3\) matrix, which involves scalar multiplication and division in each of its elements:
- The first column is obtained by multiplying each element of the first column of the original matrix by 6.
- The second column is obtained by dividing each element of the second column of the original matrix by 7.
- The third column is obtained by negating each element of the third column of the original matrix.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c4c6df5-8b96-455e-b2de-04bdb043521a%2F9d3fb950-de9a-42ac-ac41-488577834536%2Fxq83dbo_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the determinant, assuming that:
\[
\begin{vmatrix}
a & b & c \\
d & e & f \\
g & h & i \\
\end{vmatrix} = 2.
\]
**Matrix for Determinant Calculation:**
\[
\begin{vmatrix}
6a & b/7 & -c \\
6d & e/7 & -f \\
6g & h/7 & -i \\
\end{vmatrix}
\]
**Explanation:**
The problem provides two matrices. The determinant of the first \(3 \times 3\) matrix is given as 2. You are required to find the determinant of the second \(3 \times 3\) matrix, which involves scalar multiplication and division in each of its elements:
- The first column is obtained by multiplying each element of the first column of the original matrix by 6.
- The second column is obtained by dividing each element of the second column of the original matrix by 7.
- The third column is obtained by negating each element of the third column of the original matrix.
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