Mastering 12th Business Maths Exercise 8.1: Step-by-Step Solutions

Are you a student struggling with 12th Business Maths Exercise 8.1? Do you need a comprehensive guide to master this topic? You’re in the right place! In this article, we will provide you with step-by-step solutions to Exercise 8.1, along with relevant examples and case studies to help you understand the key concepts better.

Introduction

Exercise 8.1 in 12th Business Maths is an important topic that deals with matrices. Matrices are used in various fields, such as business, engineering, and computer science. Therefore, it’s crucial to master this topic to excel in your academic and professional life. This article aims to provide you with a clear understanding of how to solve Exercise 8.1, helping you achieve your academic goals.

Understanding the Basics of Matrices

Before we jump into Exercise 8.1, let’s have a quick look at the basics of matrices. A matrix is a rectangular array of numbers or variables arranged in rows and columns. Each element in a matrix is denoted by a subscript, e.g., Aij, where i is the row number, and j is the column number. The size of a matrix is defined by the number of rows and columns it has. For example, a matrix with three rows and four columns is denoted as a 3×4 matrix.

Solving Exercise 8.1

Exercise 8.1 deals with the multiplication of two matrices. To solve this exercise, follow the steps given below:

Step 1: Identify the given matrices – Let A be a matrix of size m x n, and B be a matrix of size n x p.

Step 2: Multiply the matrices – To find the product AB, multiply each element in the ith row of A by each element in the jth column of B, and add the results. Repeat this process for all rows and columns to obtain the resultant matrix.

Step 3: Verify the size – The size of the resultant matrix will be m x p.

Let’s consider an example to understand this better:

Find the product of the matrices:

Solution:

Step 1: A has dimensions 2 x 3, and B has dimensions 3 x 2.

Step 2: Multiply the matrices as shown below:

Step 3: Verify the size of the resultant matrix, which is a 2 x 2 matrix.

Therefore, the product of matrices A and B is:

Key Takeaways

In conclusion, mastering Exercise 8.1 in 12th Business Maths involves understanding the basics of matrices and following the steps given above to solve the exercise. It’s also essential to practice regularly to improve your skills. Hopefully, this article has provided you with a clear understanding of this topic and helped you achieve your academic goals.