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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Question
Two matrices A and B are given. Calculate whichever of the matrices AB and BA is defined.
![**Problem 10: Matrix Representation**
*Matrix A* is defined as a 2x2 matrix:
\[
A = \begin{bmatrix}
2 & 1 \\
4 & 3
\end{bmatrix}
\]
*Matrix B* is defined as a 2x3 matrix:
\[
B = \begin{bmatrix}
-1 & 0 & 4 \\
3 & -2 & 5
\end{bmatrix}
\]
**Explanation:**
- Matrix A consists of 2 rows and 2 columns.
- Matrix B consists of 2 rows and 3 columns.
- These matrices are used in linear algebra to perform various operations such as addition, subtraction, and multiplication, depending on the compatibility of their dimensions. For instance, the multiplication of matrix A and matrix B is possible because the number of columns in A (2) equals the number of rows in B (2), resulting in a new matrix with dimensions from the rows of A and columns of B (2x3).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb7f470a0-93f2-43bf-9ed3-2f125d19f075%2F25bbe596-f553-4bd6-8437-86507b9708f9%2F2805q58_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 10: Matrix Representation**
*Matrix A* is defined as a 2x2 matrix:
\[
A = \begin{bmatrix}
2 & 1 \\
4 & 3
\end{bmatrix}
\]
*Matrix B* is defined as a 2x3 matrix:
\[
B = \begin{bmatrix}
-1 & 0 & 4 \\
3 & -2 & 5
\end{bmatrix}
\]
**Explanation:**
- Matrix A consists of 2 rows and 2 columns.
- Matrix B consists of 2 rows and 3 columns.
- These matrices are used in linear algebra to perform various operations such as addition, subtraction, and multiplication, depending on the compatibility of their dimensions. For instance, the multiplication of matrix A and matrix B is possible because the number of columns in A (2) equals the number of rows in B (2), resulting in a new matrix with dimensions from the rows of A and columns of B (2x3).
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