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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![### Matrix Multiplication Exercise: Finding Matrix BA
Consider the matrices \( A \) and \( B \) given below:
\[ A = \begin{bmatrix} 2 & -1 \\ 3 & 4 \end{bmatrix} \]
\[ B = \begin{bmatrix} 4 & -3 \\ -1 & 2 \end{bmatrix} \]
Using the above matrices, find the product \( BA \).
### Instructions:
1. **Matrix Multiplication of BA:**
To find the product of matrices \( B \) and \( A \) (denoted as \( BA \)), perform the matrix multiplication. Recall that the element in the \( i \)-th row and \( j \)-th column of the resulting matrix is computed as the dot product of the \( i \)-th row of the first matrix (B) and the \( j \)-th column of the second matrix (A).
2. **Blank Matrix for Result:**
Fill in the values of the resulting matrix.
\[ BA = \begin{bmatrix}
\text{ } & \text{ } \\
\text{ } & \text{ }
\end{bmatrix} \]
### Detailed Steps to Calculate BA:
1. **First row, first column element** of \( BA \):
\[ (4 \times 2) + (-3 \times 3) = 8 - 9 = -1 \]
2. **First row, second column element** of \( BA \):
\[ (4 \times -1) + (-3 \times 4) = -4 - 12 = -16 \]
3. **Second row, first column element** of \( BA \):
\[ (-1 \times 2) + (2 \times 3) = -2 + 6 = 4 \]
4. **Second row, second column element** of \( BA \):
\[ (-1 \times -1) + (2 \times 4) = 1 + 8 = 9 \]
### Enter the correctly computed values:
\[ BA = \begin{bmatrix}
-1 & -16 \\
4 & 9
\end{bmatrix} \]
Fill in the provided blanks with the values computed above.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F341e5604-de03-45da-898b-0db7fbb87243%2Fd1bcc00f-0703-4eb6-8326-10bc8bd98071%2F1ywwpbo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Matrix Multiplication Exercise: Finding Matrix BA
Consider the matrices \( A \) and \( B \) given below:
\[ A = \begin{bmatrix} 2 & -1 \\ 3 & 4 \end{bmatrix} \]
\[ B = \begin{bmatrix} 4 & -3 \\ -1 & 2 \end{bmatrix} \]
Using the above matrices, find the product \( BA \).
### Instructions:
1. **Matrix Multiplication of BA:**
To find the product of matrices \( B \) and \( A \) (denoted as \( BA \)), perform the matrix multiplication. Recall that the element in the \( i \)-th row and \( j \)-th column of the resulting matrix is computed as the dot product of the \( i \)-th row of the first matrix (B) and the \( j \)-th column of the second matrix (A).
2. **Blank Matrix for Result:**
Fill in the values of the resulting matrix.
\[ BA = \begin{bmatrix}
\text{ } & \text{ } \\
\text{ } & \text{ }
\end{bmatrix} \]
### Detailed Steps to Calculate BA:
1. **First row, first column element** of \( BA \):
\[ (4 \times 2) + (-3 \times 3) = 8 - 9 = -1 \]
2. **First row, second column element** of \( BA \):
\[ (4 \times -1) + (-3 \times 4) = -4 - 12 = -16 \]
3. **Second row, first column element** of \( BA \):
\[ (-1 \times 2) + (2 \times 3) = -2 + 6 = 4 \]
4. **Second row, second column element** of \( BA \):
\[ (-1 \times -1) + (2 \times 4) = 1 + 8 = 9 \]
### Enter the correctly computed values:
\[ BA = \begin{bmatrix}
-1 & -16 \\
4 & 9
\end{bmatrix} \]
Fill in the provided blanks with the values computed above.
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