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 1:09 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.

Is there such a thing as a 3d matrix, and would we use this to find its determinant?

Yes, you can have multidimensional matrices, but they're generally called multidimensional "arrays." Here's an example of a 3d matrix that computers may use to store the colors of an image: http://www.mathworks.com/help/matlab/math/ch_data_struct5.gif Unfortunately, I can't answer your second question since I've never learned how to find determinants of matrices higher than two dimensions. Off topic, but the largest multidimensional array I've seen in practical use is six dimensions: http://blog.digilentinc.com/wp-content/uploads/2014/08/6D-array.gif

What is the name for this method?

It's called "Rule of Sarrus". It only works with 3x3 matrices.

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` Here's a link about using matrices in solving a quadratic equation: http://answers.yahoo.com/question/index?qid=20081123080813AAAsKHF

Can we find the determinant of an asymmetrical matrix like 2x3, 3x5 etc.?

No, only square (n x n) matrices have a determinant.

Main content

Course: Algebra (all content) > Unit 20

Lesson 15: Determinants & inverses of large matrices

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

Name: Determinant of a 3x3 matrix: shortcut method (2 of 2)
Uploaded: 2012-11-07T18:34:38Z
Description: Sal shows a "shortcut" method for finding the determinant of a 3x3 matrix.

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

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Sophie
Posted 11 years ago. Direct link to Sophie's post “What is the determinant u...”
What is the determinant used for exactly?
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(50 votes)
Answer
- src2043
  Posted 11 years ago. Direct link to src2043's post “It can be used to solve s...”
  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.
  Comment on src2043's post “It can be used to solve s...”
  (48 votes)
GJ Munoz
Posted 11 years ago. Direct link to GJ Munoz's post “at 1:09 what happens to t...”
at
1:09
what happens to the 4 and the 5 that was left out from the diagonals?
Button navigates to signup pageComment on GJ Munoz's post “at 1:09 what happens to t...”
(18 votes)
Answer
- ben.samuel
  Posted 11 years ago. Direct link to ben.samuel's post “The reason we copy those ...”
  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.
  Comment on ben.samuel's post “The reason we copy those ...”
  (47 votes)
Shreya Venkat
Posted 11 years ago. Direct link to Shreya Venkat's post “Is this method applicable...”
Is this method applicable to any other matrices such as a 4x4 matrix?
Button navigates to signup pageComment on Shreya Venkat's post “Is this method applicable...”
(17 votes)
Answer
- A H
  Posted 11 years ago. Direct link to A H's post “No, to find the determina...”
  No, to find the determinant of a 4x4 matrix and greater you have to use co-factor expansion.
  Comment on A H's post “No, to find the determina...”
  (26 votes)
Sambath Kin
Posted 11 years ago. Direct link to Sambath Kin's post “do we have an excercise p...”
do we have an excercise practice for calculating the determinant?
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(7 votes)
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- ben.samuel
  Posted 11 years ago. Direct link to ben.samuel's post “Someone was listening, be...”
  Someone was listening, because it's up now!
  Button navigates to signup page
  (10 votes)
Reagent X
Posted 11 years ago. Direct link to Reagent X's post “I though he said you subt...”
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?
Button navigates to signup pageComment on Reagent X's post “I though he said you subt...”
(7 votes)
Answer
- Dan
  Posted 11 years ago. Direct link to Dan's post “the actual value from the...”
  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.
  Comment on Dan's post “the actual value from the...”
  (12 votes)
Tucker Hess
Posted 10 years ago. Direct link to Tucker Hess's post “What is the name for this...”
What is the name for this method?
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(3 votes)
Answer
- Andrés Emanuel Coltre
  Posted 10 years ago. Direct link to Andrés Emanuel Coltre's post “It's called "Rule of Sarr...”
  It's called "Rule of Sarrus". It only works with 3x3 matrices.
  Button navigates to signup page
  (12 votes)
benhgift
Posted 11 years ago. Direct link to benhgift's post “Is there such a thing as ...”
Is there such a thing as a 3d matrix, and would we use this to find its determinant?
Button navigates to signup pageButton navigates to signup page
(5 votes)
Answer
- Jordan Nguyen
  Posted 9 years ago. Direct link to Jordan Nguyen's post “Yes, you can have multidi...”
  Yes, you can have multidimensional matrices, but they're generally called multidimensional "arrays." Here's an example of a 3d matrix that computers may use to store the colors of an image: http://www.mathworks.com/help/matlab/math/ch_data_struct5.gif
  Unfortunately, I can't answer your second question since I've never learned how to find determinants of matrices higher than two dimensions.
  Off topic, but the largest multidimensional array I've seen in practical use is six dimensions: http://blog.digilentinc.com/wp-content/uploads/2014/08/6D-array.gif
  Button navigates to signup page
  (4 votes)
tdjfoujtu2022
Posted 10 years ago. Direct link to tdjfoujtu2022's post “Can we only solve system ...”
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?
Button navigates to signup pageButton navigates to signup page
(3 votes)
Answer
- Petrie (Peter S. Asiain III)
  Posted 10 years ago. Direct link to Petrie (Peter S. Asiain III)'s post “`Actually we can solve qu...”
  Actually we can solve quadratic, cubic equations, etc... by using matrices as well
  
  Here's a link about using matrices in solving a quadratic equation:
  http://answers.yahoo.com/question/index?qid=20081123080813AAAsKHF
  Button navigates to signup page
  (3 votes)
Tanmay Surana
Posted 8 years ago. Direct link to Tanmay Surana's post “Can we find the determina...”
Can we find the determinant of an asymmetrical matrix like 2x3, 3x5 etc.?
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(2 votes)
Answer
- Stefen
  Posted 8 years ago. Direct link to Stefen's post “No, only square (n x n) m...”
  No, only square (n x n) matrices have a determinant.
  Comment on Stefen's post “No, only square (n x n) m...”
  (3 votes)
Τζιώρτζιης Κυπριανού
Posted 10 years ago. Direct link to Τζιώρτζιης Κυπριανού's post “Hello another great tutor...”
Hello another great tutorial :) My question is: How to find the determinant of a 4x4 matrix? I really need this because I have exam on Monday !! :) Anyone?
Button navigates to signup pageComment on Τζιώρτζιης Κυπριανού's post “Hello another great tutor...”
(3 votes)
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- MySpeed
  Posted 7 years ago. Direct link to MySpeed's post “I believe you must use th...”
  I believe you must use the other method found here: https://www.khanacademy.org/math/algebra-home/alg-matrices/alg-determinants-and-inverses-of-large-matrices/v/finding-the-determinant-of-a-3x3-matrix-method-2
  
  You can then use the method in THIS video to find the determinant of those 3x3 matrices
  Button navigates to signup page
  (1 vote)

Video transcript

As another hint, I will take the same matrix, matrix A and take its determinant again but I will do it using a different technique, either technique is valid so here we saying what is the determinant of the 3X3 Matrix A and we can is we can rewrite first two column so first column right over here we could rewrite it as 4 4 -2 and then the second column right over here we could rewrite it -1 5 0 and we could do is we could take the sum of the products of the first three top left bottom left diagonal, let me show you so the product of that that plus that plus that trying my best to draw this neatly and then from that subtract top right to bottom left diagonal so from that subtract let get a color I havent used subtract that and that and that sounds really confusing with all the diagonals i have drawn lets look at the blue ones first 4 times 5 times 0 4 times 5 times 0 plus -1 times 3 times -2 plus -1 times 3 times -2 let me put these in parenthesis plus 1 times 4 times 0 and then we gonna subtract all of these orange diagonal, we go from the top right to the bottom left so we gonna subtract we could do 1 times 5 times -2 1 times 5 times -2 and then we can subtract subtract 4 times 3 times 0 4 times 3 times 0 and then we can subtract -1 times 4 times 0 -1 times 4 times 0 and now we just evaluate this over here 4 times 5 times 0 is just 0 -1 times 3 times -2 is +6 so this is +6 1 times 4 times 0 is 0 once again and then we have 1 times 5 times -2 is -10 but we have this negative out here so it becomes a +10 then 4 times 3 times , well thats just going to be 0. and then we have -1 times 4 times 0, which is just 0 so we are left with +6 + 10 which is equal to +16