Mastering Matrices and Determinants in Mathematics

Hi guys! Welcome to today’s mathematics tutorial.
We’ll be diving into a very interesting and essential Math topic: Matrices and Determinants.

So grab your writing materials and calculators—we’re about to begin!

You can watch the full class in the video below:

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Learning Objectives

By the end of this lesson, you will be able to:

• Define matrices and determinants
• Identify the different types of matrices
• Perform basic matrix operations, including:
  • Addition
  • Subtraction
  • Multiplication (Matrix × Matrix and Matrix × Scalar)
• Calculate the determinant and inverse of both 2×2 and 3×3 matrices
• Solve linear equations using matrices

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What is a Matrix?

A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns.

To be called a matrix, the values must be neatly arranged into rows (horizontal) and columns (vertical).

Let’s take a simple example:

cssCopyEditA  B  
C  D

Here:

• We have 2 rows (Row 1: A, B | Row 2: C, D)
• And 2 columns (Column 1: A, C | Column 2: B, D)

So, this is a 2×2 matrix — 2 rows by 2 columns.

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Types of Matrices

There are several types of matrices, each with unique properties:

• Row Matrix – Has only one row
• Column Matrix – Has only one column
• Square Matrix – Number of rows = number of columns
• Diagonal Matrix – Only diagonal elements are non-zero
• Scalar Matrix – Diagonal matrix with equal diagonal elements
• Identity Matrix – Diagonal elements are 1, rest are 0
• Zero Matrix – All elements are zero

Knowing these will help you solve matrix problems faster in exams.

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Basic Matrix Operations

Matrices can be manipulated using the following operations:

➕ Matrix Addition

Only matrices of the same order (same number of rows and columns) can be added.

➖ Matrix Subtraction

Just like addition, subtraction requires the matrices to be of the same size.

✖️ Matrix Multiplication

You can multiply:

• A matrix by another matrix
• A matrix by a scalar (single number)

Remember: For matrix multiplication to work, the number of columns in the first matrix must equal the number of rows in the second matrix.

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Finding Determinants

The determinant is a special number that can be calculated from a square matrix.

2×2 Matrix Determinant:

Given:

lessCopyEdit| a  b |
| c  d |

Determinant = ad - bc

3×3 Matrix Determinant:

More complex, but follows a systematic process (Laplace expansion or Sarrus’ Rule).

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Finding the Inverse of a Matrix

The inverse of a matrix is like the reciprocal of a number. Not all matrices have inverses.

A matrix has an inverse only if its determinant is not zero.

Inverse of a 2×2 Matrix:

If:

lessCopyEdit| a  b |
| c  d |

Then the inverse is:

markdownCopyEdit(1 / (ad - bc)) × | d  -b |
                  | -c  a |

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Solving Linear Equations with Matrices

Matrices provide a neat and efficient way to solve systems of linear equations using methods like:

• Matrix Inversion Method
• Cramer’s Rule
• Row Reduction (Gaussian Elimination)

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Watch more educational videos and past questions: https://youtube.com/@allcbts

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Final Thoughts: Why You Must Master Matrices

Matrices and determinants are not just for passing exams—they’re used in computer science, engineering, economics, cryptography, and more!

Whether you’re preparing for WAEC, NECO, JAMB, IJMB, or JUPEB, understanding matrices gives you a serious academic advantage.

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Related Videos:

• Understanding Waves and Properties in Physics

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