3x3 Matrix Determinant Worksheet For Easy Calculation

Are you struggling to calculate the determinant of a 3x3 matrix? Look no further! This article will provide you with a comprehensive worksheet to help you easily calculate the determinant of a 3x3 matrix.

What is a 3x3 Matrix Determinant?

A 3x3 matrix determinant is a value that can be calculated from the elements of a 3x3 matrix. It is used to determine the solvability of a system of linear equations and to find the inverse of a matrix.

Why is it Important to Calculate the Determinant of a 3x3 Matrix?

Calculating the determinant of a 3x3 matrix is important because it helps to:

• Determine the solvability of a system of linear equations
• Find the inverse of a matrix
• Calculate the area of a parallelogram
• Determine the volume of a parallelepiped

How to Calculate the Determinant of a 3x3 Matrix

To calculate the determinant of a 3x3 matrix, you can use the following formula:

Det(A) = a(ei − fh) − b(di − fg) + c(dh − eg)

where a, b, c, d, e, f, g, h, and i are the elements of the matrix.

Step-by-Step Calculation

1. Write down the matrix:

a  b  c
d  e  f
g  h  i

2. Calculate the minor of each element:

Minor of a: (ei − fh)
Minor of b: (di − fg)
Minor of c: (dh − eg)

3. Multiply each minor by its corresponding element:

a(ei − fh)
b(di − fg)
c(dh − eg)

4. Add up the products:

a(ei − fh) + b(di − fg) + c(dh − eg)

5. Simplify the expression to get the determinant.

Worksheet for 3x3 Matrix Determinant Calculation

Here is a worksheet to help you practice calculating the determinant of a 3x3 matrix:

Matrix 1:

2  3  4
5  6  7
8  9  10

Matrix 2:

1  2  3
4  5  6
7  8  9

Matrix 3:

3  2  1
6  5  4
9  8  7

Calculate the determinant of each matrix using the formula above.

Gallery of 3x3 Matrix Determinant Calculation

Matrix Determinant Calculation Examples

We hope this article and worksheet have helped you to easily calculate the determinant of a 3x3 matrix. Practice makes perfect, so be sure to try out the worksheet and examples above. If you have any questions or need further clarification, please don't hesitate to ask. Share this article with your friends and classmates to help them with their matrix calculations.