3x3 Matrix Determinant Issues (why always 3 times greater than they should be?)

[MorSher]

May I ask where I am going wrong, in my calculations, when the determinants of my 3x3 matrices continue to be 3 times greater than they should be? I am able to achieve the correct answer when using the Rule of Sarrus Method, but when trying to work through using a Matrix of Minors, Matrix of Cofactors, Transpose, etc process, my determinant continues to be 3 times larger than it should be. I am just not sure where I continue to go wrong, in my calculations. Any advice would be appreciated.

 

[Deleted member 4993]

May I ask where I am going wrong, in my calculations, when the determinants of my 3x3 matrices continue to be 3 times greater than they should be? I am able to achieve the correct answer when using the Rule of Sarrus Method, but when trying to work through using a Matrix of Minors, Matrix of Cofactors, Transpose, etc process, my determinant continues to be 3 times larger than it should be. I am just not sure where I continue to go wrong, in my calculations. Any advice would be appreciated.

We cannot tell you that - since we cannot see your work. Please share your work in detail, for us to investigate and pin-point any error in your calculations.

 

[MorSher]

We cannot tell you that - since we cannot see your work. Please share your work in detail, for us to investigate and pin-point any error in your calculations.

 

[MorSher]

Work

View attachment 9077
Here is an example of my work.

 

[mmm4444bot]

Here is an example of my work.

Did you make changes here (from the work shown previously), or is this second image a duplicate of the first? :cool:

 

[Dr.Peterson]

Here is an example of my work.

That helps a lot. It's easy to see what you're doing wrong, now.

When you use the cofactor expansion, you are supposed to use only one row.

What you are doing is all three rows (that is, all elements). So you have found the same determinant three times.

Look at your sum:

2 - 24 + 15 - 0 + 17 - 24 - 9 - 0 + 2
\_________/ \___________/ \_________/
    -7           -7           -7

You should only do one of those.

See here and here for examples:

To find the determinant of the matrix A, you have to pick a row or a column of the matrix, find all the cofactors for that row or column, multiply each cofactor by its matrix entry, and then add all the values you've gotten.

When you need to evaluate the determinant of a matrix you do not need to find all the nine cofactors.

You only need to find the cofactors of the three elements in the row or column that you have chosen.