How To Find the Determinant of a 3x3 Matrix - The Easy Way!
The Organic Chemistry Tutor・5 minutes read
To find the determinant of a 3x3 Matrix using a shortcut method, write the matrix columns, multiply the diagonals, and calculate the determinant value. The shortcut method simplifies the process compared to the older method, which is better suited for determining the determinant of a 4x4 Matrix.
Insights
- The shortcut method for finding the determinant of a 3x3 Matrix involves multiplying diagonal numbers and performing specific arithmetic operations, leading to a quicker and more efficient calculation process.
- While the shortcut method works well for 3x3 Matrices, a longer method is more appropriate for determining the determinant of a 4x4 Matrix, highlighting the importance of choosing the right approach based on the matrix's dimensions.
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Recent questions
How do you find the determinant of a 3x3 Matrix?
By multiplying diagonal numbers and following a specific formula.
What is the shortcut method for finding determinants?
Multiply diagonal numbers and follow a specific formula.
When should you use the older method for determinants?
For determining the determinant of a 4x4 Matrix.
Can you provide an example of finding a determinant using the shortcut method?
Yes, by multiplying diagonal numbers and following a specific formula.
Where can I find more math videos on matrices and related subjects?
Check the links in the video description for a playlist.
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Summary
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Shortcut Method for 3x3 Matrix Determinants
- To find the determinant of a 3x3 Matrix using a shortcut method, start by writing the matrix's columns: 52 -6, 354, and 7 89. Then, multiply the diagonal numbers from top left to bottom right: 5*5*9, 3*8*-6, and 7*2*4. Add the first three products and subtract the sum of the second set of products to get the determinant value, which in this case is -737.
- For another example with the matrix columns 857, 469, and 3 -28, repeat the process by writing the columns, multiplying the diagonal numbers, and calculating the determinant value. In this case, the determinant value is -77.
- The shortcut method simplifies finding the determinant of a 3x3 Matrix compared to the older, longer method. The older method is more suitable for determining the determinant of a 4x4 Matrix.
- Access more math videos, including algebra and pre-calculus topics, by checking the links in the video description for a playlist on matrices and related subjects.
