Grade 11 Maths Unit3: 3 .2 .5 Multiplication of Matrices & Exercise 3. 6 & 3 .7 |Saquama

Introduction

This tutorial focuses on the multiplication of matrices, a key concept in Grade 11 mathematics. Understanding how to multiply matrices is essential for solving various problems in algebra and applications in fields such as physics and engineering. This guide will provide you with clear, step-by-step instructions to help you grasp matrix multiplication and complete exercises related to it.

Step 1: Understanding Matrix Dimensions

Before diving into multiplication, it's crucial to understand the dimensions of matrices.

• A matrix is defined by its number of rows and columns.
• The dimensions are written as m x n, where m is the number of rows and n is the number of columns.
• To multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second matrix.

Practical Tip

• Always check the dimensions before attempting to multiply matrices to ensure the operation is valid.

Step 2: Performing Matrix Multiplication

Once you've confirmed the matrices can be multiplied, follow these steps to perform the multiplication:

1. Identify the Matrices: Let's say you have Matrix A (m x n) and Matrix B (n x p).
2. Create Result Matrix: The resulting matrix (C) will have dimensions m x p.
3. Calculate Each Element:
   • For each element C(i, j) in the resulting matrix, calculate it using: [ C(i, j) = \sum_{k=1}^{n} A(i, k) \times B(k, j) ]
   • This means you multiply each element of the i-th row of Matrix A by the corresponding element of the j-th column of Matrix B and sum the products.

Example

If Matrix A is:

| 1 2 |
| 3 4 |

And Matrix B is:

| 5 6 |
| 7 8 |

Then the resulting Matrix C would be calculated as follows:

• C(1,1) = (15) + (27) = 5 + 14 = 19
• C(1,2) = (16) + (28) = 6 + 16 = 22
• C(2,1) = (35) + (47) = 15 + 28 = 43
• C(2,2) = (36) + (48) = 18 + 32 = 50

Thus, Matrix C is:

| 19 22 |
| 43 50 |

Step 3: Practicing with Exercises

To reinforce your understanding, practice with Exercises 3.6 and 3.7 from your textbook. These exercises will provide you with various matrices to multiply.

• Start with smaller matrices to build confidence.
• Gradually move to more complex matrices as your skills improve.

Common Pitfalls

• Forgetting to check matrix dimensions before multiplication.
• Miscalculating the sums or forgetting to sum all products.

Conclusion

Matrix multiplication is a fundamental skill in mathematics that requires practice and attention to detail. By understanding the dimensions of matrices and following the outlined steps for multiplication, you can solve related exercises with confidence. Continue practicing with exercises and seek additional problems to enhance your skills further. Happy studying!