All About Matrices

Adding, Subtracting, Multiplying, and Finding Determinants

What is a Matrix?

By definition, a matrix is any rectangular array of variables or constants in horizontal rows and vertical columns. Matrices can also be used matrix equations, matrix forms used to represent a system of equations. The determinant of a matrix is a number that is calculated from a square matrix. A square matrix is when the matrix has the same number of columns as it does rows, such as a 2x2 matrix, or a 3x3 matrix. The determinant is useful for things such as systems of linear equations, or finding the inverse of a matrix.

Adding and Subtracting Matrices

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Adding and Subtracting Matrices

When adding and subtracting matrices, the numbers of rows and columns must first be the same. For example, a 2x3 (2 rows by 3 columns) matrix can only be added to a matrix that is also 2x3. To perform the operation, you simply add or subtract the numbers that are in corresponding spots of each matrix. Examples are shown below:
Addition With Matrices - Demonstration/Tutorial
Subtraction With Matrices - Demonstration/Tutorial

Multiplying Matrices

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Multiplying Matrices

When multiplying matrices, first, you must make sure that the number of columns of matrix A, and the number of rows of matrix B are equal. Then you multiply each row by each column and put the products into a new matrix. The resulting matrix should have the number of rows of matrix A, and the number of columns of matrix B. For example, if you multiplied a 3x4 by a 4x2, the matrix will be 3x2. An example is shown below:
Multiplication With Matrices || Demonstration

Determinants

Finding the Determinant of a Square Matrix

Determinants can always be found in square matrices. They do not result from non-square matrices. They can be found by in each of the scenarios below by the following steps:

In a 2x2 matrix -

  1. Multiply the two numbers that are diagonal to each other
  2. Multiply the two numbers that are diagonal to each other in the opposite direction
  3. Subtract the second product from the first product


Video example below:

Finding the Determinant of a 2x2 Matrix || Demonstration

In a 3x3 matrix -

  1. Take the first two columns of the matrix and copy them to the right of the matrix
  2. Multiply the three numbers that are diagonal to each other in each of the columns
  3. Add those three numbers together
  4. Multiply the three diagonals going in the opposite direction
  5. Subtract those three numbers from the sum of the other numbers


Video example below:

Finding the Determinant of a 3x3 Matrix || Demonstration

What Was Learned?

  • What a matrix is
  • How to add matrices together
  • How to subtract matrices
  • How to multiply matrices
  • How to find the determinant of a matrix


Below is a quick tutorial on how to use matrices on a calculator -

Matrices on a Calculator Basics || Demonstration

Upcoming Assessments -

Quiz #4 - Monday, December 7th

Test #2 - Thursday, December 10th