Simpler 4×4 Determinant | Matrix Transformations | Linear Algebra | Khan Academy

Calculating a 4×4 determinant by putting in in upper triangular form first.

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Simpler 4×4 Determinant | Matrix Transformations | Linear Algebra | Khan Academy

29 Comments on “Simpler 4×4 Determinant | Matrix Transformations | Linear Algebra | Khan Academy”

  1. Well this method is only useful with matrices which were intentionally made to be easily solvable, I mean good luck using this method in this 4×4 (54, 46, -85, 156), (-23, -2, -121, -69), (-61, 203, 40, -183), (16, 12, 1, 48), the answer is 0 btw.

  2. Now hold the phone… I thought multiplying a row by a scalar C also scales the determinant by C… SAL!

  3. Excellent videos , thanks. By the way when this guy pronouncing vowels he reminds me Stewie Griffin from family guy hoho

  4. Hey guys, check out this app, it computes the determinant of any matrix from 2×2 to 7×7 and it can make up matrices so you can practice!

  5. can anyone help me to find out the inverse of 4*4 matrix easily except row operation???

  6. excuse Khan, what happens if you switch the 1st and last row. Do you still turn the matrix into a negative.?

  7. If we swap two lines, the sign of the determinant flips aswell.
    Is this only for triangular form? Or does it have a specific rule?

  8. beinging maths studying is well good for studying the matrix study easy to well understanding super experience fot students

  9. Why was R_2 X R_3 performed instead of R_4 X R_2 ? Usually you use partial pivoting and use the largest absolute value for swaps to avoid subsequent round off errors.

    Also R_3 has 0,3,1,0 when you swap and already contains a pivot at 1, so it means one less flop..

  10. I have some questions out of this video… Some things you did here have no proper explanation, like swapping the rows (I’m pretty sure some swaps will give different answers)

  11. at 6:56 to make the 6 in the last row 0, why cant you perform this operation (-3R1 + R4). When I did this i ended up with the final answer as 36.


    this “upper triangular” method does not seem to work. I do it by hand for other problems and I can’t get the right answer. even on matlab, if you enter the matrix you used for your example and then use the “triu” function, you get a diagonal product of 30!!!!

    same with other examples.. plz help me, anybody!

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