May 2021 2 134 Report
Determinant of a triangular matrix?

Now, I understand algebraic operations within matrices and determinants of matrices, but for some reason I can't seem to get this determinant right through making it a triangular matrix and then multiplying the elements along the diagonal.

First off, I start with:

| 1 3 9 |

| 1 -1 8|

|1 4 4 |

The determinant is apparently 21, but when I make it a triangular matrix I get 84.

My work for making it triangular:

| 1 3 9 |

| 1 -1 8|

|1 4 4 |

becomes

| 1 3 9 |

| 0 -4 -1|

|0 1 -5 |

I subtracted the 1st row from the 2nd for my new 2nd, and the 1st row from the 3rd for my new 3rd.

Next:

| 1 3 9 |

| 0 -4 -1|

|0 0 -21 |

I multiplied the 3rd row by 4, added it to the 2nd row and declared that as my new 3rd row. Now, the determinant of my triangular matrix is (1)(-4)(-21) = 84 which is not 21.

What am I doing wrong?

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