Matrix Operations Answer Key
Introduction
In this article, we will provide the answer key for matrix operations. Matrix operations are an essential part of linear algebra and are used in various fields such as mathematics, physics, engineering, and computer science.
Matrix Operations
1. Matrix Addition
Example: Find the sum of the following matrices:
A = | 1 2 | | 3 4 |
B = | 5 6 | | 7 8 |
Answer:
A + B = | 1+5 2+6 | | 3+7 4+8 | = | 6 8 | | 10 12 |
2. Matrix Subtraction
Example: Find the difference of the following matrices:
A = | 1 2 | | 3 4 |
B = | 5 6 | | 7 8 |
Answer:
A - B = | 1-5 2-6 | | 3-7 4-8 | = | -4 -4 | | -4 -4 |
3. Matrix Multiplication
Example: Find the product of the following matrices:
A = | 1 2 | | 3 4 |
B = | 5 6 | | 7 8 |
Answer:
A × B = | 1(5) + 2(7) 1(6) + 2(8) | | 3(5) + 4(7) 3(6) + 4(8) | = | 19 22 | | 43 50 |
4. Scalar Multiplication
Example: Find the result of multiplying the following matrix by a scalar:
A = | 1 2 | | 3 4 |
Scalar: 2
Answer:
2A = | 2(1) 2(2) | | 2(3) 2(4) | = | 2 4 | | 6 8 |
Conclusion
In this article, we have provided the answer key for matrix operations. Matrix operations are an essential part of linear algebra and are used in various fields. We hope this article helps you understand the concepts of matrix operations.
Note: This article is not a comprehensive guide to matrix operations. It is recommended to study the concepts of matrix operations in more detail to gain a deeper understanding of the subject.
