How To Find The Determinant of a 4x4 Matrix

[@TheOrganicChemistryTutor]

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MR. Organic Chemistry Tutor, thank you for an excellent video/lecture on Finding the Determinant of a 4x4 Matrix. This is a classic problem in old fashion Linear Algebra/Systems.

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Wow ,now I can find the determinant of a 4*4, thanks sir.

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[@miz3567]

It may be good practice to draw straight lines for determinant instead of square brackets. 5*[A] means different thing to 5*|A|

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:V

[@PenandPaperScience]

That is correct :)

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cut him some slack , like u wouldn't be here if u knew more then him

[@aarohganjoo1676]

@@abdullahsehgal1614 hey you have a point but proper notation is very important. A matrix and determinant are not the same thing, so it would be incorrect to use square brackets when computing a determinant

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@@abdullahsehgal1614 jeez, calm down dude, it was just a suggestion.

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[@dermakol8543]

Recommend a bit of gaussian elimination - if you add third row to first and third row multiplied by 2 to second and fourth, you will get a nice (0, 0, -1, 0) column and you only have to calculate a determinant of one 3x3 matrix.

[@marcelukeje3510]

It doesn't work that way. It only works for equations

[@dermakol8543]

Yeah, it does, adding a multiple of a row doesn't change anything. The other row operations do, but it is still just a scaling by constant you can keep track of.

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Matrix is easy to work with but one of the most difficult to memorize after the class is over due to tons of components and terminology. One saving grace for me is “array” 😂

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This is a GREAT way to find determinants

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[@CMSLine8]

Love from India. I have fully understood after going through your video. I used to become very uncomfortable when I saw 4×4 order determinants.

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One recommendation......you can use Sarrus rule for determinants and solve it quickly within 2 minutes

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[@_ndot]

Explanation on the signs for each operation. Everything should be an addition and the sign comes from multiplying (-1)^(row-index + column-index). So, if you were to use the second row you should have: 2 x ((-1)^(2+1)) x |minor at M2,1| + 5 x ((-1)^(2+2)) x |minor at M2,2| + ... 2 x (-1) x |minor at M2,1| + 5 x (1) x |minor at M2,2| + ... -2 x |minor at M2,1| + 5 x |minor at M2,2| + ... This part gives you the sign for row 2 column 1: ((-1)^(2+1)) = -1. The easiest way to think about it, is to add the indices if its odd is - if its even is +. Row 2 Column 1 => 2 + 1 = 3 => odd - Row 2 Column 2 => 2 + 2 = 4 => even + Row 2 Column 3 => 2 + 3 = 5 => odd - Row 2 Column 4 => 2 + 4 = 6 => even + ...

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