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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![To perform the matrix multiplication as given in the problem, we have two matrices:
Matrix \( A \):
\[
\begin{bmatrix}
1 & 2 \\
-1 & 3
\end{bmatrix}
\]
Matrix \( B \):
\[
\begin{bmatrix}
0 & 2 \\
1 & 4
\end{bmatrix}
\]
Matrix \( T \) is the product of \( A \) and \( B \), denoted \( T = A \cdot B \).
The task is to find the element at position \( t_{21} \) of the resulting matrix \( T \).
### Matrix Multiplication Process:
1. **Calculate \( t_{21} \):**
- \( t_{21} \) is located in the second row and first column of matrix \( T \).
- To find this, take the dot product of the second row of \( A \) and the first column of \( B \):
- \( (-1 \times 0) + (3 \times 1) = 0 + 3 = 3 \)
Thus, the element at position \( t_{21} \) in the resulting matrix \( T \) is **3**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F855418f3-d840-444d-b866-5c675da27c94%2Fe53c8c44-bf57-43ee-a314-ee9eb826c517%2Fhoj2vrs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:To perform the matrix multiplication as given in the problem, we have two matrices:
Matrix \( A \):
\[
\begin{bmatrix}
1 & 2 \\
-1 & 3
\end{bmatrix}
\]
Matrix \( B \):
\[
\begin{bmatrix}
0 & 2 \\
1 & 4
\end{bmatrix}
\]
Matrix \( T \) is the product of \( A \) and \( B \), denoted \( T = A \cdot B \).
The task is to find the element at position \( t_{21} \) of the resulting matrix \( T \).
### Matrix Multiplication Process:
1. **Calculate \( t_{21} \):**
- \( t_{21} \) is located in the second row and first column of matrix \( T \).
- To find this, take the dot product of the second row of \( A \) and the first column of \( B \):
- \( (-1 \times 0) + (3 \times 1) = 0 + 3 = 3 \)
Thus, the element at position \( t_{21} \) in the resulting matrix \( T \) is **3**.
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