Select the row of A and the column of B whose dot product is the entry AB5,4 in the product AB. J 1 0 0 0 1 10 1 1 1000 1 0 1 1 T 1 0 1 1 1 0 1 B = |immuni 1 1 0 1 0 1 1 1 1 0 1 1 1 1 1 1 0 1 0 1 0000
Select the row of A and the column of B whose dot product is the entry AB5,4 in the product AB. J 1 0 0 0 1 10 1 1 1000 1 0 1 1 T 1 0 1 1 1 0 1 B = |immuni 1 1 0 1 0 1 1 1 1 0 1 1 1 1 1 1 0 1 0 1 0000
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 Dot Product Exercise**
**Objective:**
Select the row of matrix \( A \) and the column of matrix \( B \) whose dot product is the entry \( AB_{5,4} \) in the product \( AB \).
**Matrix \( A \):**
\[
A = \begin{bmatrix}
1 & 1 & 0 & 0 & 0 \\
1 & 1 & 1 & 0 & 1 \\
1 & 1 & 0 & 0 & 0 \\
1 & 0 & 1 & 0 & 1 \\
1 & 1 & 1 & 0 & 1 \\
\end{bmatrix}
\]
**Matrix \( B \):**
\[
B = \begin{bmatrix}
1 & 1 & 1 & 1 \\
1 & 1 & 0 & 1 \\
0 & 1 & 1 & 1 \\
1 & 0 & 1 & 0 \\
0 & 0 & 0 & 0 \\
\end{bmatrix}
\]
**Instructions:**
- Identify which row of matrix \( A \) and which column of matrix \( B \) correspond to the entry in the product matrix \( AB \) at position \((5, 4)\).
- Calculate the dot product of the selected row and column to find the value of the entry.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcede8746-e52f-4eaf-bfc2-0cf286297e7e%2Ff4e702a4-f8ff-4e12-96dd-886eb2a1e826%2Fcef5my_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Matrix Dot Product Exercise**
**Objective:**
Select the row of matrix \( A \) and the column of matrix \( B \) whose dot product is the entry \( AB_{5,4} \) in the product \( AB \).
**Matrix \( A \):**
\[
A = \begin{bmatrix}
1 & 1 & 0 & 0 & 0 \\
1 & 1 & 1 & 0 & 1 \\
1 & 1 & 0 & 0 & 0 \\
1 & 0 & 1 & 0 & 1 \\
1 & 1 & 1 & 0 & 1 \\
\end{bmatrix}
\]
**Matrix \( B \):**
\[
B = \begin{bmatrix}
1 & 1 & 1 & 1 \\
1 & 1 & 0 & 1 \\
0 & 1 & 1 & 1 \\
1 & 0 & 1 & 0 \\
0 & 0 & 0 & 0 \\
\end{bmatrix}
\]
**Instructions:**
- Identify which row of matrix \( A \) and which column of matrix \( B \) correspond to the entry in the product matrix \( AB \) at position \((5, 4)\).
- Calculate the dot product of the selected row and column to find the value of the entry.
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