 Quandaries and Queries

I have to find the determinant of the following matrix

 -2 3 1 2 4 -3 0 -2 5 1 4 2 1 -3 5 2 3 4 -1 2 6 0 3 2 -4

Hi,

(I am displaying the matrix as a table since it's easier for me to do that.)

When I looked at this matrix I decided to work with the second column since it contains two zeros. I performed three operations

1. Multiply the first row by -1 and add it to the fourth row.
2. Multiply the third row by -1 and add it to the first row.
3. Multiply the first row by -2 and add it to the third row.

This gave me

 -6 1 0 5 -1 -3 0 -2 5 1 16 0 1 -13 7 4 0 3 -3 -2 6 0 3 2 -4

which is -1 times

 -3 -2 5 1 16 1 -13 7 4 3 -3 -2 6 3 2 -4

Here again I decided to work with the second column. I performed the three operations

1. Multiply the second row by 2 and add it to the first row.
2. Multiply the third row by -1 and add it to the fourth row.
3. Multiply the second row by -3 and add it to the third row.

This gave me

 29 0 -21 15 16 1 -13 7 -44 0 36 -23 2 0 5 -2

Thus I have -1 times

 29 -21 15 -44 36 -23 2 5 -2

Looking at the third row I decided to add the first column to the third column to get

 29 -21 44 -44 36 -67 2 5 0

At this point I decided to expand along the third row and I finally got the value of the determinant to be 319.

Cheers,
Penny

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