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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
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.
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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