Lesson Notes By Weeks and Term v4 - SHS 2

Lesson Video

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Performance objectives

• Define the inverse of a matrix.
• Calculate the adjoint of a 2x2 matrix.
• Find the inverse of a 2x2 matrix.
• Verify if two matrices are inverses of each other.

Lesson summary

This lesson introduces the concept of the inverse of a matrix. Just as we can find the reciprocal (or multiplicative inverse) of a number to "undo" multiplication (e.g., the inverse of 5 is 1/5), we can find an inverse for certain matrices. This powerful tool is not just a mathematical curiosity; it is fundamental to solving complex systems of linear equations. In Ghana, this can be used to model and solve real-world problems in business, such as determining the unit cost of products, in cryptography for securing information, and in computer graphics. We will learn a systematic method to find the inverse of 2x2 and 3x3 matrices using the determinant and the adjoint matrix.

Lesson notes

A. Introduction to the Inverse of a Matrix

In basic algebra, the multiplicative inverse of a number 'a' is '1/a' because `a * (1/a) = 1`. The number '1' is the multiplicative identity.

In the world of matrices, the Identity Matrix (I) acts like the number '1'. For a 2x2 matrix, I = $\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$. For a 3x3 matrix, I = $\begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix}$.

The inverse of a square matrix A, denoted as A⁻¹, is the matrix that, when multiplied by A, results in the identity matrix. > AA⁻¹ = A⁻¹A = I

Evaluation guide

• Find the inverse of a matrix using linear transformation.
• Collaborative Learning, Experiential Learning, Problem -based Learning, Project -based
• conceptual
• understanding Activity: Inverse of a matrix