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### Course: Algebra (all content)>Unit 20

Lesson 15: Determinants & inverses of large matrices

# Determinant of a 3x3 matrix: shortcut method (2 of 2)

Sal shows a "shortcut" method for finding the determinant of a 3x3 matrix. Created by Sal Khan.

## Want to join the conversation?

• What is the determinant used for exactly?
• It can be used to solve systems of equations with cramers rule. It can be used to represent the cross product (a type of vector multiplication). But I believe there is more to it.
• at what happens to the 4 and the 5 that was left out from the diagonals?
• The reason we copy those columns is just for visual simplicity. What's really happening is that the diagonals are wrapping around, like in Pac Man.

So the 4 is actually being used by the blue diagonal starting at 1 and the orange diagonal starting at -1. Likewise, the 5 that seems to be unused is really the 5 that is right in the middle of the matrix.
• Is this method applicable to any other matrices such as a 4x4 matrix?
• No, to find the determinant of a 4x4 matrix and greater you have to use co-factor expansion.
• do we have an excercise practice for calculating the determinant?
• Someone was listening, because it's up now!
• I though he said you subtracted the result of the first set of diagonals from the second? So shouldn't the answer be -4, as 6-10=-4?
• the actual value from the second set of diagonals is -10. So you are subtracting a negative which is the same as adding the positive.
• What is the name for this method?
• It's called "Rule of Sarrus". It only works with 3x3 matrices.
• Is there such a thing as a 3d matrix, and would we use this to find its determinant?
• Can we only solve system of linear equations through matrices . Can't we solve system of quadratic ,cubic ,quartic or any degree equations through matrices?
• `Actually we can solve quadratic, cubic equations, etc... by using matrices as well`