College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.3: Matrix Algebra
Problem 66E
Related questions
Question
Compute (a) and (b) using the matricies
Transcribed Image Text:### Mathematical Expressions
Here are the mathematical expressions provided:
a) \( 5A - 3B \)
b) \( BD \)
- **Expression a)**: This represents a linear combination of variables \(A\) and \(B\) where \(A\) is multiplied by 5 and \(B\) is multiplied by -3. It is often used in algebra to denote operations involving variables.
- **Expression b)**: This represents the product of variables \(B\) and \(D\). It indicates that the variables should be multiplied together.
No graphs or diagrams accompany these expressions.
![## Matrices Introduction
In this section, we will learn about matrices and examine four specific examples. A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. It is essential in various fields, including mathematics, physics, and engineering.
### Example Matrices
Below, we have four matrices labeled \( A \), \( B \), \( C \), and \( D \).
#### Matrix \( A \)
\[
A = \begin{bmatrix}
4 & -1 & 0 \\
2 & 3 & -2 \\
-5 & 2 & 1 \\
\end{bmatrix}
\]
#### Matrix \( B \)
\[
B = \begin{bmatrix}
1 & 5 & -1 \\
6 & 2 & -3 \\
1 & 0 & 4 \\
\end{bmatrix}
\]
#### Matrix \( C \)
\[
C = \begin{bmatrix}
5 & 1 \\
-3 & 0 \\
\end{bmatrix}
\]
#### Matrix \( D \)
\[
D = \begin{bmatrix}
1 & 3 \\
5 & -1 \\
0 & -2 \\
\end{bmatrix}
\]
### Explanation of Matrices
1. **Matrix \( A \)** is a 3x3 matrix (3 rows and 3 columns).
2. **Matrix \( B \)** is another 3x3 matrix (3 rows and 3 columns).
3. **Matrix \( C \)** is a 2x2 matrix (2 rows and 2 columns).
4. **Matrix \( D \)** is a 3x2 matrix (3 rows and 2 columns).
Understanding these matrices is fundamental to applications in linear algebra, where operations such as addition, multiplication, and finding determinants are common tasks.
Feel free to explore these matrices and try performing operations like addition, subtraction, and multiplication to deepen your understanding.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F336090ec-d2ca-4d15-a2ae-85a71ff5580d%2F1c5d2870-d7dd-42bb-93bb-691e625b658f%2F3sfz0e4_processed.png&w=3840&q=75)
Transcribed Image Text:## Matrices Introduction
In this section, we will learn about matrices and examine four specific examples. A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. It is essential in various fields, including mathematics, physics, and engineering.
### Example Matrices
Below, we have four matrices labeled \( A \), \( B \), \( C \), and \( D \).
#### Matrix \( A \)
\[
A = \begin{bmatrix}
4 & -1 & 0 \\
2 & 3 & -2 \\
-5 & 2 & 1 \\
\end{bmatrix}
\]
#### Matrix \( B \)
\[
B = \begin{bmatrix}
1 & 5 & -1 \\
6 & 2 & -3 \\
1 & 0 & 4 \\
\end{bmatrix}
\]
#### Matrix \( C \)
\[
C = \begin{bmatrix}
5 & 1 \\
-3 & 0 \\
\end{bmatrix}
\]
#### Matrix \( D \)
\[
D = \begin{bmatrix}
1 & 3 \\
5 & -1 \\
0 & -2 \\
\end{bmatrix}
\]
### Explanation of Matrices
1. **Matrix \( A \)** is a 3x3 matrix (3 rows and 3 columns).
2. **Matrix \( B \)** is another 3x3 matrix (3 rows and 3 columns).
3. **Matrix \( C \)** is a 2x2 matrix (2 rows and 2 columns).
4. **Matrix \( D \)** is a 3x2 matrix (3 rows and 2 columns).
Understanding these matrices is fundamental to applications in linear algebra, where operations such as addition, multiplication, and finding determinants are common tasks.
Feel free to explore these matrices and try performing operations like addition, subtraction, and multiplication to deepen your understanding.
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