Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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![### Determinant Calculation Exercise
**Instructions:** Fill in the blanks with the appropriate numbers to calculate the determinant.
### Problem (a)
Given the following 2x2 matrix:
\[
\begin{vmatrix}
3 & 4 \\
-7 & 9 \\
\end{vmatrix}
\]
Fill in the blanks to find the determinant:
\[
= \_\_\_\_\_ \cdot 9 - \_\_\_\_\_ \cdot 4 = \_\_\_\_\_
\]
### Problem (b)
Given the following 3x3 matrix:
\[
\begin{vmatrix}
1 & -1 & -3 \\
3 & -4 & 1 \\
0 & 2 & 0 \\
\end{vmatrix}
\]
Fill in the blanks to find the determinant:
\[
= \bowtie 1 \cdot ( \_\_\_\_\_ \cdot 0 - \_\_\_\_\_ \cdot 2) \bowtie 3 \cdot ( \_\_\_\_\_ \cdot 0 - \_\_\_\_\_ \cdot -3) \bowtie 0 \cdot ( \_\_\_\_\_ \cdot 1 - \_\_\_\_\_ \cdot -3) = \_\_\_\_\_
\]
In the provided matrix, each box should be filled with the appropriate number to calculate the determinant. The exercise aims to practice the formula for calculating the determinant of matrices.
### Explanation (b):
• The determinant of a 3x3 matrix is computed by:
\[
\begin{vmatrix}
a & b & c \\
d & e & f \\
g & h & i \\
\end{vmatrix}
= a(ei - fh) - b(di - fg) + c(dh - eg)
\]
• Each step follows the expansion by minors along the first row.
Have fun solving these determinant calculations!](https://content.bartleby.com/qna-images/question/8c4e41d9-a3ac-4d29-97cc-72954cf84754/e1d917a4-a4e6-48bd-9c8e-0a8e0cf081f0/r4ca3k.png)
Transcribed Image Text:### Determinant Calculation Exercise
**Instructions:** Fill in the blanks with the appropriate numbers to calculate the determinant.
### Problem (a)
Given the following 2x2 matrix:
\[
\begin{vmatrix}
3 & 4 \\
-7 & 9 \\
\end{vmatrix}
\]
Fill in the blanks to find the determinant:
\[
= \_\_\_\_\_ \cdot 9 - \_\_\_\_\_ \cdot 4 = \_\_\_\_\_
\]
### Problem (b)
Given the following 3x3 matrix:
\[
\begin{vmatrix}
1 & -1 & -3 \\
3 & -4 & 1 \\
0 & 2 & 0 \\
\end{vmatrix}
\]
Fill in the blanks to find the determinant:
\[
= \bowtie 1 \cdot ( \_\_\_\_\_ \cdot 0 - \_\_\_\_\_ \cdot 2) \bowtie 3 \cdot ( \_\_\_\_\_ \cdot 0 - \_\_\_\_\_ \cdot -3) \bowtie 0 \cdot ( \_\_\_\_\_ \cdot 1 - \_\_\_\_\_ \cdot -3) = \_\_\_\_\_
\]
In the provided matrix, each box should be filled with the appropriate number to calculate the determinant. The exercise aims to practice the formula for calculating the determinant of matrices.
### Explanation (b):
• The determinant of a 3x3 matrix is computed by:
\[
\begin{vmatrix}
a & b & c \\
d & e & f \\
g & h & i \\
\end{vmatrix}
= a(ei - fh) - b(di - fg) + c(dh - eg)
\]
• Each step follows the expansion by minors along the first row.
Have fun solving these determinant calculations!
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